[bogwog]

Alternatively, the "sport" in esports is the genre (FPS, Moba, Fighting, etc), and the "leagues" are the individual games. Yes, the specific rules and mechanics of each game are vastly different even within the same genre, and strategies will be different, but skills like leadership, reaction time, hand-eye-coordination, etc will be used similarly across all games. Even with an open source game, it's likely each league will want to make changes to the base game anyways.

Maybe an open source game could work for smaller "leagues" that don't have the resources to develop an entire game from scratch (and assuming there's even a demand for a small league like that), but even then forking/building atop an open source game is still a lot more work than just using an existing commercial game that has more flexible multiplayer options (and so long as there aren't licensing issues)