Under Iranian law, any child of an Iranian man is an Iranian citizen unless they've explicitly renounced their citizenship after the age of 25 and the Iranian government has accepted their renunciation, and the US State Department would lean on that to insist he is technically not stateless.

To be clear, I think this is a cruel act, and shouldn't be legal, and he may well be right that he practically can't risk to try to claim his Iranian citizenship even if he wanted to, but purely technically he's probably not legally stateless.