The unremitting savagery of commerce and industry, insofar as that savagery does not represent the development or refinement of historical cultural practices, may from time to time get fresh blood and thus fresh impetus, from coincident practices of co-existing cultures. Information about such practices, to include information about headhunting, cannibalism, and other so-called barbarisms, provides the prerequisite for those practices to make their mark upon the language of the culture impressed by them.
So the adoption of 'headhunter' and, more to the point, 'headhunting', for metaphorical use in the US to signify "employee recruiter" and "employee recruiting" was the natural offshoot of widespread dissemination of information about the supposed literal and symbolic significance of the practice in other cultures, followed by the diffusion of that conceptual framework into language in the US. Such abstractions as dissemination and diffusion are, however, ultimately unsatisfying when it comes to picking apart the development of specific terms in language. For more concrete, and thus more satisfying evidence of the processes of linguistic development, the collection of particular uses exampling such development suffices.
In the case of the development of 'headhunter' and 'headhunting' from literal significance to metaphorical use in the sense of "recruiter" and "recruiting", that development was greatly assisted by widespread dissemination, in the US, of information about the original cultural practice. For example, in the late 1800s, it was widely reported in the US that the Dayaks, a headhunting tribe, believed "every person [they] kill in this world will be [their] slave in the next" (Clarion Ledger, Jackson, Mississippi, 4 Oct 1893; paywalled). For people holding such a belief, headhunting would quite literally be considered recruitment — for the afterlife.
The putative religious belief of the Dayaks that by headhunting they recruited slaves, or servants, for their support in the afterlife, was variously reported. For example, in the 8 Oct 1893 Nebraska State Journal (paywalled; emphasis mine) it took this more elaborate form:
The Dyaks, or headhunters, of Borneo, believed in a heaven but had the curious superstition that they would be happy there in proportion to the number of servants they had, and as each man whom they beheaded in this world was bound to them as a slave forever in the next, the head-hunting became a sort of religious frenzy.
Setting aside the close parallel between the Dayak's recruitment of servants for the afterlife by 'headhunting', and corporate recruitment of employees in this life by 'headhunting', the development of metaphorical uses of 'headhunting' illustrates divergent understanding of the term. In one case, 'headhunting' signifies the culling of the labor force. This is attested, for example, by OED's earliest citation (1909) for use of 'headhunting' in the sense of the "action or practice of targeting people for recruitment, now esp. by identifying and approaching highly skilled or experienced personnel already employed elsewhere, and typically carried out by a recruitment agent or agency on an employer's behalf", noted as "orig[inally] U.S.":
1909 Mahoning Disp. (Ohio) 5 Mar. 1/5 The traction company has ceased head hunting. They laid off a lot of good men.
That metaphorical use of 'headhunting' to mean "getting rid of employees" appears much earlier. For example, in the 24 Mar 1885 Democrat and Chronicle (Rochester, New York; paywalled; bold emphasis mine),
MANNING GOES HEAD-HUNTING
Secretary Manning has begun a thorough investigation into the treasury department routine, with a view to reducing the force and simplifying work.
Another example from the 7 June 1887 issue of the Oakland Tribune (Oakland, California; paywalled; emphasis mine):
But the lobby has a theory, whence derived it is hard to say, that the Council is head hunting, and that early in July the heads will begin to fall, high as some of them now wag.
In the 1890s metaphorical uses of 'headhunting' with the opposite sense, that is, with the meaning of "recruiting" as opposed to "getting rid of", began to appear in political contexts. Examples include this from the 20 May 1891 Salt Lake Tribune (Salt Lake City, Utah; paywalled; bold emphasis mine):
Those persons, Republicans or Democrats, who are negotiating with the Mormon chiefs for the transfer of Mormon votes to the Republican and Democratic parties respectively...admit to themselves...that all THE TRIBUNE has said of the political serfdom in which the masses of the church are held by the church leaders is true. The Saints wait for orders...with the order, any Democrat of them would vote a Republican ticket, or vice versa, or would refuse to vote either. We ask the persons engaged in this head-hunting by proxy to take notice that the way they are going about this work is not the American way....
Another example from the 3 Feb 1899 Sedalia Weekly Democrat (Sedalia, Missouri; paywalled; emphasis mine):
STOP THE STRIFE
The democrats in the Missouri general assembly should proceed at once to stop the useless strife in which they are engaged.
In order to do this it will be necessary to stop some other things.
For instance, the conservative members of the party should insist that all efforts to build up a personal political machine must cease, and that the schemes to enable one faction to control municipal affairs in the big cities and thus capture the delegations to the state conventions must be defeated.
And then this "head hunting" must cease, too.
Another example from the 8 Mar 1904 Harrisburg Telegraph (Harrisburg, Pennsylvania; paywalled; emphasis mine):
WHICH WILL MEET THE CHAMPION?
About this time every year the Democratic factions in Dauphin county go head hunting. They like the sport and as the casualties are confined to their own camp the sanguinary conflict is allowed to proceed without hindrance.
Meanwhile, uses of the 'headhunting' metaphor with the opposite sense continue, as this from the 22 Oct 1905 Evening Star (Washington DC; paywalled; emphasis mine) shows:
The Phillippine civil service is also an expensive one. The principal cuts are being made by the "head-hunting committee" in this direction.
The constant drumbeat behind all the metaphorical uses, and quite evidently inspiring them, is widespread and frequent reporting about the cultural practice of literal headhunting, and ongoing efforts to eradicate that practice. In the early 1900s, however, before, during and after the 1904 St. Louis World Fair, frequent and widespread reporting on a particular touring exhibition of a headhunter village, complete with real live headhunters, began to dominate among those reports. A representative advertisement was commonly accompanied by an 'informative' article:
Soon, apologists for, or at least equivocators of, headhunting begin to appear in the popular news. This is a specimen from the 8 Feb 1906 Globe Republican (Dodge City, Kansas; paywalled; emphasis mine):
MURDER IN THIRST FOR GAIN
Ways of Civilization Likened to Those of Savages
After years of residence among the head hunters of Borneo an Englishwoman writes of them as follows: "I don't want to stand up for head-hunting; it isn't nice. The civilized nations call it murder, and it is murder. But are we to throw stones? Aren't the means we take to satisfy our unquenchable thirst for gain, murder? Tailoring, shirt-making, straw plaiting, lace and box and nailmaking and how many more? Do any of them bear looking into if we want to feel that, as a country, we do not murder? Isn't the whole destruction of body, soul and spirit which drink and gambling and immorality are carrying on hourly at our very doors, and inside many of them, filling our hospitals and lunatic asylums, and graves — isn't that murder? And in our murder are any good qualities necessary. None! But fighting brings out the noblest parts of a savage, and in his home life love and content reign; but civilized murder means misery and discontent and homes turned to hell."
Such apologetics, or equivocations, soon come with hats (ad from the 18 Apr 1906 The Journal Times, Racine, Wisconsin; paywalled):
Use of 'headhunting' in the sense of "recruiting" in political contexts continues and, in terms of frequency, accelerates alongside equivocating articles. Here is another, perhaps more persuasive equivocation, from the 24 Apr 1908 Democrat and Chronicle (Rochester, New York; paywalled; emphasis mine):
IT WORKS BOTH WAYS
A number of scientists are now engaged in a laudable study of the characteristics of the inhabitants of the Philippine Islands, and incidentally, it is understood, a collection of skulls is being made for the Peabody Museum. Their operations have been chiefly confined to Visaya, and the skull-collecting industry is meeting with some adverse criticism.
Lieutenant-Colonel Hadsell, of the Nineteenth United States Infantry, who has seen service in the Philippines, has raised a question which would appear to be worthy of consideration by the enthusiastic Yale anthropologists who are busy with the skulls of the Visayans. After reminding them that there are many Visayans in the United States, he pictures these curious strangers as making collection of the skulls of New Englanders for the museum of the Visayan College at Cebu, which has existed almost as long as Yale University.
Colonel Hadsell follows the anthropological fad to its legitimate conclusion, and pictures the Visayans as becoming so greatly absorbed in their studies as not to content themselves with bones from New England graveyards, and indulging in the head-hunting proclivities of their more savage fellow islanders.
Head-hunting, not unlike missionary endeavor, is much a matter of the point of view. Obviously, from the standpoint of Yale, it is more pleasant to hunt the heads of Visayans than it would be to have the Visayans hunt the heads of New Englanders.
...who shall repress the curiosity of the Visayans regarding the conformation of the New England skull?
It was not, however, only transitional metaphorical uses, in this case uses refering to the recruitment of voters for and by political machinations, that paved the way for the development and adoption of the terms 'head-hunter' and 'head-hunting' in the more contemporary senses of "employee recruiters" and "employee recruiting"; rather it was the entire process of acculturative diffusion accruing from dissemination of information on the putative practices and beliefs of another culture.