Very few players in the world get paid for playing eSports. It's much easier making money off of tricking teenagers that they can earn a living by playing eSports. You're probably better off writing about or gamecasting eSports than to actually play it. Some of these gaming sites take in some serious revenue solely on advertising.
These 'pro' teams are run in such a way that transportation/accomodation costs to and from events are covered for the players with the help of sponsorships and maybe a small cut of the prize money. The only way you're making money is if you're winning some high profile tournaments. To get 'pro' in today's top games usually means you have to have set aside 5-6hrs a night practicing (or have been practicing similar games for many years) just to get anywhere near winning prize money. Kids are better off doing their homework, or if you're old enough, play online poker.