The full paragraph in The Man of Property in which the quoted sentence appears runs as follows:
A Forsyte will require good, if not delicate feeding, but a Dartie will tax the resources of a Crown and Sceptre [the restaurant where the party consisting of Montague Dartie, his wife Winifred (Forsyte) Dartie, Irene Forsyte, and Philip Bosinney are about to dine]. Living as he does, from hand to mouth, nothing is too good for him to eat; and he will eat it. His drink, too, will need to be carefully provided; there is much drink in this country 'not good enough' for a Dartie; he will have the best. Paying for things vicariously, there is no reason why he should stint himself. To stint yourself is the mark of a fool, not of a Dartie.
The person whose thoughts we are privy to in this paragraph is Monty Dartie, who is ordering dinner for the party of four. Dartie himself is a wastrel who has married into money (in the form of Winifred Forsyte) but nevertheless lives "from hand to mouth"—that is, precariously—because of his propensity to gamble dangerously and to drink excessively. Literally, one who lives "from hand to mouth" is quite accustomed to eating anything available, whatever its quality may be, and we might very well say of such a person "nothing is too bad [or meager or coarse or unappetizing] for him to eat."
The idea that "nothing is too good for him [a Dartie] to eat" is thus a kind of inversion of the adage that beggars can't be choosers; in effect, Galsworthy says, beggars authorized to spend other people's money can be as choosy as they wish. In this context, "nothing is too good for him to eat" amounts to saying "he will not deny himself anything on the menu by judging that it is too fancy or too expensive or too extravagant."
Of the two interpretations that the poster offers for the original phrase "nothing is too good for him to eat," the first ("All are good enough for him to eat") is certainly much closer to the mark than the second ("There is not any good thing [or food] for him to eat"), but it doesn't capture Galsworthy's central point, which is the idea that Dartie feels entitled to the best of everything. This same notion of entitlement lies at the core of the common (and more general) English expression "nothing is too good for [him/her/them]."