There are PROFESSIONAL video game players?
Yes. And it can be quite profitable too.
Depending on the game, millions of dollars of prize winnings and sponsorship went to certain gamers last year. The global prize money for 2016 $95mil.
The biggest trend in the prize money pool is where the money is earnt. Whilst you can make some money from competing online, gamers are expected to travel to tournaments (of which, there are now many!). ‘The International 2016’ DOTA2 championship last year had a prize fund of over $18mil (which is a larger pool than Wimbledon), whereas currently the biggest sim racing prize fund was $1mil for the Las Vegas eRace hosted by Formula E.

Why are the potential earnings higher in person?
There are a few reasons for this:
Ticket sales – Depending on the event, tickets can be sold for fans to watch in-person. eSports events have sold out entire arenas to people hoping to watch an epic game with a great atmosphere. Personalisation – It’s hard to love an avatar. Like any version of sports, it’s the human element that brings viewers.
Sponsorship - Companies can sponsor equipment and prize money. There's a much greater incentive for them to invest if their equipment is on show.
So why should I run an event and give away prizes?
Because everyone in the world, with access to the required equipment, can win it. That is huge. Your brand and your event/competition can have such a huge reach that people from across the world can access it. It’s not the same as traditional sports, where for many there are multitudes of barriers to entry.
Take this one example: GT Academy. No prize money, just an awesome project that captured the imagination of their audience.
GT Academy was the result of a deal between Nissan and Sony. The competition allowed people from around the world to compete online at first with their Playstations to qualify for regional finals and finally for the chance to become a Nissan-backed racing driver.
Here are the awards and recognition this particular campaign produced:
2013 AUTOSPORT Awards, Pioneering and Innovation Award 2012 Cannes Lions International Festival of Creativity, Bronze Lion, Best Use of Branded Content 2011 Cannes Lions International Festival of Creativity, Gold Lion, Best Use of Branded Content 2011 ‘Campaign’ magazine Media Awards, Best Transport Campaign 2011 ‘Campaign’ magazine Media Awards, Best Media and Entertainment Campaign 2011 Media Week Awards, Best International Campaign
eSports event can be a hugely beneficial investment for companies. Just make sure it's organised by professionals!