I've toyed with the idea of doing some type of recurring Q&A but that felt a bit pretentious. A virtual happy hour once a month might be fun. I actually think your idea of a game on a zoom call is really interesting. That way there's less one-directional focus and we can all just hang out and do something together. And if people have questions I can answer them too.
One other option is doing some type of writer meetup where there isn't any selling or courses. Just a hangout session.
Occasionally, a stranger asks me for a selfie and I feel like the coolest guy in the world haha.