Bob's response in your example does not pertain to the truth or falsity of what Alice said, so his response isn't an argument at all. It's not really meaningful to say whether it is fallacious.
A fallacious argument from Bob might go along the lines of, "no I shouldn't, because you haven't stopped yourself". This is fallacious because it purports to show that cheaters should not stop cheating, but (at best) what it actually concludes is that Alice does not think cheaters should stop cheating. Whether Alice thinks her own claim is correct does not affect whether it is actually correct, because Alice's claim does not concern her own beliefs.
But Bob's response to Alice in your example is not a counter-argument; it is a proposal. Bob has not disputed that he should stop cheating, he instead proposes that both of them stop cheating together, and declares that this is the condition on which he will do what Alice said he should do.
Of course, Alice might not trust that Bob will uphold his end of such a bargain, but that's neither here nor there. Insofar as "I'll stop cheating if you do" is a proposition with a truth value (rather than a speech act), for all we know, it is true; perhaps Bob will stop cheating if Alice does. Something being true doesn't necessarily mean that an argument is logically valid, but Bob doesn't suggest any premises from which he claims the truth of his statement follows, so there is just no argument for us to assess the validity of.
Now, language and communication are complicated, and it's certainly possible that depending on the context and on Bob's tone of voice, expressions, body language or so on that when Bob says "I'll stop cheating if you do", perhaps what he really means (and what Alice understands him to mean) is "No, I don't need to stop cheating, because you aren't stopping". That would be a fallacy, and in real life we might rebuke Bob on the basis that we know what he meant even though he didn't say it out loud. But that's interpersonal skills, not logic.