To conclude that a person's criticism of X has rebutted by applying that criticism to them is an informal logical fallacy. You have not responded to their argument, at all.

They presented a definition of bigot and assurted that Islam met that definition.
Instead of addressing the conclusion of their argument (~Islam is bigoted), you responded by asserting that OP met that definition.

Just answer this question: If your assertion is accepted as true, does that mean that their assertion is not true?
(i.e. if OP is bigoted, therefore Islam is not.)

Whether you agree with OP's assertion or not, this response is a poor excuse for an argument.