no, he's just an idiot that doesn't know how to argue...didnt put enough effort into his posts... it was probably a natural reaction to double down.
however, he did not follow the rules... maybe someone should have told him what the rules were before banning him, not everyone (read most) reads the TOS.
I have seen lots of people accuse others of cheating and not get banned, AND they always reminded them of the TOS...
I'd say this looks like crap from Chess.com and likely wont be giving them any more of my money.