No, Chess is not gambling.
It's a game with a win/loss/draw result.
I don't agree that there is any luck whatsoever; it's purely skill-based. If I played Hikaru or Magnus 1,000 times, I would lose 1,000 times. Therefore, there is no luck involved.
If you say Chess is gambling, then any sport or competition between individuals or teams is gambling, which it isn't.
Gambling does not only have to do with money. Luck and probability also relate to gambling. Chess, especially speed formats, involve luck. I could go into a blitz session hoping to gain 50 rating points... It might happen, it might not.