PewDiePie seems more than a pro-game. I haven't encountered him that often, but he seems to be creating games, and advertising (reviewing other games).

That's what I'm saying. He's not a competitive gamer in competitions, but he games as his profession. He's a celebrity gamer, rather than a competitive gamer. It's not the review itself people watch him for, it's the playing and bantering during the review. It's different than just a review-article.

However If we go back to the tennis allegory: Tennis makes most of their money from: Ticket sales to spectators Non tennis-playing products (fashion).

They also make money from promotion. Ads on the side of the court, and the competitors using specific "approved" sponsor equipment, like Titleist. Even what the contestants are wearing and drinking matters. Gatorade? Propel? Purina water? Aquafina? These are provided for by the Tennis tournament. Companies pay for those product placements.

Then there's also licensing the matches to TV companies; who put their TV ads inbetween the matches.

I seems that most of the pro gaming money is to directly advertise games that are being played. Is there a lot of "outside" money powering this?

Teams are individually sponsored, and wear their sponsors' logos.
Ads during the matches sell unrelated videogames (to an already gaming-interested audience) even from different companies, videogaming equipment, and things of that nature.
The monitors, mice, mousepads, keyboards, game controllers, headphones/microphones, and computers are all carefully chosen and carefully positioned to promote the manufacturers who are paying for that equipment to be used. Alienware/Dell, Bose, Logitech, NVidia, AMD, Intel, etc...

Yea, there is outside money. Watch a professional tournament, and keep your eyes open. If you're observant enough, you'll be able to spot dozens of explicit sponsers, and dozens of implicit sponsers, even without the outright ads.