To begin with, I should note that when Untermann says the word is descended from an Aryan root, he is referring to what we would nowadays call Indo-European. The Aryan languages are a sub-branch of the Indo-Aryan or Indo-Iranian languages, one of the main branches of Indo-European; but back then, it was sometimes used for the family as a whole.
It seems almost certain that he is talking not about the word manger (a trough for horses or cattles), nor manager, but rather monger, which does indeed mean a dealer or a salesman.
The Old English word for a monger was not quite manger as Untermann put it, but rather mangere, at least in all the dictionaries I’ve been able to find it in, such as Bosworth’s. It’s quite possible manger was a known variant as well, though.
Manger does not have an altogether certain etymology further back than Proto-Germanic, where it originates in the verb *(ga-)mangō(ja)n-. Etymonline and Wiktionary both connect this verb to the Latin noun mangō ‘dealer, (slave) trader’, connected to mangōnium ‘displaying of wares’, which in turn they suppose was borrowed from Ancient Greek μάγγανον (mánganon), which refers to a “means of charming or bewitching others”.
This is a somewhat roundabout etymology, hinging on the notion that traders trying to trick their customers by embellishing and cheating with their wares goes back to antiquity. I do believe this is true, but there is no actual evidence that it gave rise to this development of meanings here.
Another possibility is that given in Guus Kroonen’s Etymological Dictionary of Proto-Germanic, which takes *(ga-)mangōjan- to be a derivation from the abstract noun *ga-manga- from the weak verb *mangjan- ‘mingle, mix’, which is not attested outside Northwest European (that is, Germanic and Balto-Slavic).
The development here would be:
- Base verb *mang-jan- meaning ‘mix, mingle’
- From that was derived an abstract noun *ga-mang-a- meaning ‘mixing, mingling, multitude of things or people mixed together’ (Old English ‘multitude, assembly, crowd, marketplace’, Middle Dutch ‘mingling together, company’; Modern English among is from Old English on ġemang ‘in assembly/crowd’)
- From that was derived a weak verb *(ga-)mang-ō-jan- meaning something along the lines of ‘go and do that thing you do in crowds/assemblies/marketplaces’. In Dutch, this meant ‘mingle, exchange, argue’; in Old Norse (manga) and Old English (ġe-mangian), it meant ‘barter, trade, deal’.
- From that verb was derived an agent noun with the productive ending -ere, i.e., (ġe-)mangere ‘dealer, tradesman’.
This development is definitely more plausible, speaking in purely formal terms: each step of the development is fairly clearly visible, and the only part that is not an obvious semantic extension is going from ‘crowd/assembly’ to ‘bartering/trading’, but this development has many typological parallels elsewhere. The Ancient Greek ἀγορά (agorá), equivalent to the Roman forum, for example, originally meant ‘assembly’, but the word was used as the basis for derivations such as ἀγοράζω (agorázō) meaning ‘trade, buy’.
The only trouble with this explanation is that it leaves Latin mangō unexplained. The Latin form is remarkably similar to the Germanic forms, but it may actually just be coincidence. The fact that Latin mangō not only means ‘slave trader’ (thence ‘trader’ in general) but also ‘furbisher, polisher’ might indicate that it really does come from the Greek word. Polishing something up is one way of ‘cheating’ to make it look better.
If Robert Beekes’ Etymological Dictionary of Greek is to be believed, and in this case I do think it is, μάγγανον has many traits of what Beekes calls ‘pre-Greek’: Ancient Greek words that clearly share a great many traits and characteristics with each other, but look decidedly non-Indo-European—presumably words taken in from one or more unknown substrate languages spoken in the Balkans when the Greeks arrived there.
In particular, one frequently observed pattern is that the same root may show up in parallel derivations with its final consonant prenasalised and voiced or plain and aspirated. In this case, that would connect μάγγανον to μηχανή (mēkhanḗ) ‘machine, mechanic’. Μάγγανον has a plethora of meanings, of which some are more focused on the aspect of deceiving, enchanting, bewildering, etc.; and others focus on the implement used to deceive, enchant, bewilder, etc.
If μάγγανον and μηχανή are indeed connected, they probably do come from a root that meant something like ‘trick, ruse’—but there is nothing to suggest that this is an Indo-European root. It looks much more like a ‘pre-Greek’ root.
So in conclusion, I would say the answer is that Untermann’s statement is not backed up by the facts we have available now.
The most likely scenario is that monger comes from a root meaning ‘intermix, mingle’ (possibly Indo-European in origin, but only attested in the Germanic and Balto-Slavic branches). The ‘deceive’ root which he mentions is almost certainly not an Indo-European root, but a ‘pre-Greek’ substrate root, and though it is deceptively similar to the Germanic root, they are not related.
Writing in 1907, however, Untermann would have had no way of knowing this. Many of the pieces of evidence which have led to this conclusion were not available at that time, and at the time he wrote, his statement would almost certainly represent the communis opinio of historical linguistics.