If I were to run a webgame on a mobile browser, would it just go into the Web platform? It's the same game, just different controls.

You mean running it in a browser on a mobile device? I’ve done that before and put it as web.

Id say you do it because some web games tend to have a web and an android version which are in the same leaderboards so, to be consistent, Id use web whenever you use a mobile browser and only android/iOS for apps

Which game?

Any web game that can be ran on mobile

Most games just have one platform, but if mobile or web has a distinct advantage I would add mobile as a platform so it can be filtered. But 99% of the time they are the same.