Earning money for being best in game?!

People play feeder tournaments and hope to get into a big sponsored one like they just had in Vegas.

Top players can make $100K a year or more with endorsements but it's only a tiny fraction of players that are that good and even less that are also photogenic, charismatic and can stay out of trouble.

There's also Twitch, etc which requires less game skill but more charisma and attractiveness.

I know a game where every "player" earns some money and there are no winners - it's called "idling free shіt", you should try it!

Try pwnwin.com

As it's not e-sport what you are looking for, it might be poker. I would not suggest it, but it certainly matches your criteria above (playing from home, even on the move, getting money if you are good at it). On the other hand, you can lose a lot, unlike with the others.