They may have a slightly stronger case for defamation or similar because chess.com said the account was closed for "fair play violation", but still.

The case for defamation is weaker than normal here, since chess.com (from what I can tell) never told anyone but the user that they considered them a cheater--there's no statement being made that can have the quality of being defamatory in the first place, except the statement being made by the user.