I find that very worryingly vague. In my reading though, that only applies to YouTube itself ("the Service"). It seems to be saying that your Google account can lose access to YouTube, not that you can lose access to your Google account.
The thing that was apparently against unspoken Youtube policy here was this kind of interactive, emote-driven streaming. But I get the impression Markiplier didn't get banned, only their fans.
It's bizarre and alarming.
But that's beside the point. Losing the ability to receive email is not something that should ever happen under any circumstances.