Short Answer
Attacking the opponent directly is clearly ad hominem. The more specific question is 'is there a sub-type such that snobbery is a key characterization?'. According to WP, this may qualify as an appeal to motive since by characterizing the opponent as elitist or snobbish, one is purporting to speak to the motive of the critic instead of the argument of the critic.
Long Answer
My argument is A, but don't believe critics of A, since they are snobs (and snobs {don't care about you and me, understand you and me,...}!
This seems to be a fair characterization of your explanation. Clearly, the claimant isn't addressing the counterargument at all, but is speaking to the nature of the opponent, implicitly questioning their motives. Rhetorical technique goes beyond logical argumentation precisely because it considers the pathos of an argument. Once rhetorical technique enters this territory, it is no longer logical, but psychological. We might even speculate as to what that psychology might be.
There is strong support in sociology, which studies how people interact, that human beings function in "tribes". Such sources of group identity are instrumental to a person's behavior so much so, that group identities are often justifications for immoral acts, such as when the NSDAP murdered 6 million people of Jewish descent based on their purported race. Claims of snobbery or elitism tap into that same sense of social rejection.
Such thinking is often referred to as in-group/out-group behavior precisely because of the commonality of such reasoning motivating behavior. Because of the nature of a dominance hierarchy, there's a certain game-theoretic advantage to populist rhetoric since the top of a hierarchy is generally numerically smaller than the base of a population. This sort of rhetoric is exemplified in US politics by recent movements expressing dissatisfaction with the current state of affairs by the 99%ers who often attack the motives of the wealthy by using the loaded language '1%er' when arguing positions often riding on the presumption that the ultrawealthy are out of touch, elitist, or condescending and have a different set of untoward motives.