You are still confusing the GM and Coach. The GM is never the coach.

The fact that the coach can be fired because of the team’s performance means that he isn’t the GM.

A GM is a primarily business role, a coach is not. Regardless of who is considered a “GM” in the nascent esports scene doesn’t mean they are a GM, just that only they are in name.

In C9, Jack is the GM. He is the primary person they contact when determining how much to pay someone and who is acceptable for a price.

In TL, Dodo is not a GM. He is someone who is familiar with the League team, and helps make decisions with how TL runs. By your own logic, if Dodo can’t be a GM, because if Jatt is supposedly the “management aspect” of the org, what would Dodo’s purpose be?