There are things called routers that...route traffic. A dumbed down version is routers talk to other routers to find out what they know about.
If a game server you connect to matches you with someone in Japan, your computer sends a packet with the address in Japan attached to it. Your home router probably has no clue where that is, so it goes to its upstream router and asks if they know, this process repeats until one figures it out and you get a route.
This all happens very quickly, and it's why people say the Internet routes around damage.
There's like three leagues in my suburban area, so I imagine quite a lot.
I believe there's zero difference between sports and sports other than audience size and length of time the leagues have been around.
Now a single streamer playing a single player game and mostly engaging with the audience? That's a different matter, and probably more like drive time radio than anything.