Well, at least one major adult cam site banned streaming games a few years back due to copyright concerns. Not sure about other sites but I suspect they'd end up having to do the same thing if it caught on there; the plausible deniability of being on a games streaming site is important if you want to be able to stream games, since it's at best a bit of a copyright grey area and developers don't have the same incentive to permit adult streamers as they do plain game streamers.
The "pools, hot tubs, beaches" exception was a (stupid) loophole and they should just close it (I suspect that this is the end result moving forward, eventually). The hard part for Twitch is figuring how to do this with out appearing sexist.