Last time I checked, they had a website where you can access your generated content. You should just log in with your Discord account.

I doubt that Discord is the driver behind their success. They could have used IRC and people would go out of their way to engage with them because what they're doing was so interesting at the time. If they get banned from Discord, the vast majority of the community will move to wherever they go.

This is a different situation than something like app stores where if Apple bans you, that's the end of your company. Users simply cannot get your app from somewhere else, at least not without giving an Android vendor $1000. Nobody will do that.