1 - The companies that make the game. Whether it's Riot and Blizzard selling slots in their leagues for eight figures, Valve using their annual tournament to sell in-game cosmetics, or all the companies ultimately owning broadcast rights to their game, this is the biggest difference between esports and traditional sports.
The New York Yankees and Los Angeles Dodgers make money because they sell their own tickets and broadcast rights to their games; even though MLB does control the streaming revenue, they share it out to teams and ultimately have to bow to the wishes of a majority of team owners. What you don't see is a single company MLB inc that owns the copyright to the game of baseball, sells broadcast rights to all teams themselves, charges teams to play in the league, and can kick teams out of the league at a whim. That's the situation in esports.
2 - Individual players, with streaming. Players can first make a name for themselves in competitions, then stream on their own Twitch channel for revenue. This is not that different from athletes acting as social media influencers and signing endorsement deals, but the biggest difference is that by streaming on Twitch, they appear side-by-side with tournament broadcasts. It's as if LeBron's instagram account where he streamed his workouts and pickup games were just one change-of-the-channel away from ESPN, and people would consider it normal to flip between the game and individual player streams.
Lots of esports orgs, as part of signing players, get a big cut of the player's streaming revenue. But the revenue for an individual player's twitch stream, while great for an individual, usually isn't going to be significant enough to maintain a whole organization, and when a player brand does get big enough that their stream could sustain an org - that's when the player will be heavily incentivized to go independent, and make more money from streams than they do from competing.
Ultimately, I think esports has a bright future - overall total viewership continues to rise, even though some games like League of Legends - which is more than a decade old now - are starting to fade. It's just the business models of the offline sports world don't carry over, and that's especially apparent with these organized teams.