Esport has a physical component where every millisecond and mouse/keyboard action can decide the game. Chess doesn't, except maybe blitz.
Hearthstone is a popular esport where games are decided by strategy (and maybe luck) rather than physical reflexes. So that does not seem to be a differentiator.
Tbh Hearthstone would probably not be chosen considering the amount of RNG and the fact that it's not very popular compared to other games.
But I agree, it's more comparable to chess and could be played as a tabletop game with little if any adjustments.
My vote is for blitz chess + allowing competitors to kick the opponent under the table.