I think the google group and the GitHub tracker answer the same need (Premake related development) and that's why the group is deserted.
I'd be in favor of removing the link to the group from the Readme since we don't really look it up.
As for another communication channel, I'm in favor of Slack or another alternative. I never used Discourse but it looks to be more like a forum?
I think a chat would answer to another type of communication that GitHub issues are not designed for.
IMO, a chat would contains smaller support requests than the issue tracker that I wouldn't mind looking it up if I have 10-15 minutes of free time.
And if larger questions comes up, we can always redirect people to the tracker.
Another thing is enabling people to contribute.
Posting a first issue / PR on a repo is always a big step (at least for me). I think it would ease this process if people can interact in a less "heavy" environment first.