I think the world champion withdrawing from a major tournament and accusing a young player of cheating seemingly out of spite causing an overall very childish reaction in the community as a whole will tarnish the reputation of the game significantly, yes.
I don’t think chess is in any risk of disappearing but it was on a significantly upward trajectory when it comes to popularity that this kind of antic may noticeably dent if not reverse.
I think there is two pronged issues here. First is reputation of the players involved. Specially those attacking.
And then overall putting even the events in question. If he cheated? Who else have cheated? And how common is cheating? Could it even be that the popular names are cheaters too? After all it takes one to know one...
