Amazon would be one of the major winners if esports takes of due to so much of it being broadcast via twitch, I have no idea what amount of revenue stream twitch contributes to but I imagine it hardly enough to move the needle unfortunately due to the sheer size of amazon.
Modern times group owns a controlling interest in several esports tournament franchises, they are listed on the Swedish exchanges, DYOR of course, I personally don’t have plans to buy any stock of them (nor have any idea how tbh!)
I guess Tencent are well placed with Riot games and Fortnite, I believe that Riot games runs and broadcasts most of the major league of legends high tier play. Again tencent is massive though so may not be much of a needle mover
One of the tough things about this industry is defining it to an extent and working out where the money is going to go. Games development/broadcast and media/tournaments are all different industries in and of themselves.