He's not wrong.
I mean yeah, sure, race is not really a thing (or at least, no more than a social construct) but besides that he's right.
Look at me, I'm not religious, my parents were not religious and neither were grandparents. In fact, they are anti-religious atheist communists. I'm still considered a Jew though.
Anyway, the question what is and who is a Jew is actually not as simple as you might think, but I'm not sure this thread is a best place to have this discussion. It's fairly clear how racist dickheads answer that question.
p.s.
This wiki article is a good start if you're curious about that question -
https://en.wikipedia.org/wiki/Who_is_a_Jew?