The new one, yes. The old one runs on Kirby.
We decided to switch to Discourse because it offers a lot of features our self-built old forum didn’t have. The new forum improved discussion a lot.
So as Sonja said: You can build a forum with Kirby, but it is work. 
The old Kirby forum code should be archived in the Kirby site repository, maybe you can use it as a starting point.