It seemed odd that there was no way to do that - and there actually "isn't", sometimes, because it can be unavailable in the UI...
For anyone else who has the same problem, there's an "Enable Profile Management" switch under Settings. IDK what the default for it is, but if that's off you'll need to enable it to get the "Profiles" section to appear so you can remove a game.
(not actually edited, but the forum seems to sometimes remove line spacing the first time I post something, even though it's still there when I edit the post and just have to re-submit it without doing anything else...) :)
