I believe games like chess would be the best option for PvP games. There can be other games based on skill or luck and if I am not wrong there used to be a dice game on Primedice during its initial days where we were allowed to play against fellow players on the primedice platform and there was a small fees which was charged though, not sure about that though.
By the way this topic was started years ago but I am shocked no PvP games have been made yet, maybe because the house wants the player to lose money to them instead of other players but with the help of a small fees per bet there can be platforms who might offer these games.
Chess can certainly be a better solution. But I'm not sure that Chess will be very popular. After all, it's not a game for everyone and games can take a very long time. I once went to chess school and I remember that once a game lasted more than 6 hours. I think a lot of people would get bored with such a long game. We need a game that lasts no more than an hour and a half.