Not sure if they IP ban you because it's not reliable. Most internet providers don't give you a static IP, you get a new one every time you connect to the internet.

I've been IP banned before from some Counter Strike (1.6) servers back in the day because they though I was cheating (I just learned the AK's recoil pattern), all I had to do was restart the router to play again.

I recently visited a forum for the first time and I wanted to comment but I couldn't because I was IP banned. Probably because someone trolled there with the IP that I ended up receiving.

Me and my friends got banned from an online game because we logged in from school computers and sent each other resources. They thought they were one person's alt accounts, which was forbidden. This was before wifi became commonplace so I guess they assumed everyone used their own internet.

I suspect that your IP is just one data point that they use to try to identify you if they do this sort of thing. Your browser (or their app) provides tons of information like screen resolution, device id, extension list, plugged in device list etc. These can identify you quite accurately.