Displaying empathy and compassion for your friends is really important,definitely not a bad thing. And at the same time, shouldering another person's problems and absorbing their stress will eventually wear you out if it's happening a lot/you're not able to do the same in return.
There are a couple of strategies, like be supportive but put the responsibility back on their shoulders. Something like, "You're a smart person. I am confident you will figure this out and come out stronger than ever." Or whatever makes most sense for the situation.
You could also set boundaries/an alternative while still employing compassion. At a time (not game night, in the moment) you guys are just chill and hanging out or chatting, you could say something like 'Hey, you know I'm here for you, right? Why don't we set up a time to just chat and catch up about <insert issues> so that we can focus on stress free fun on game night?'
It's also really important you don't take on a role you're not qualified for. Suggest professional counselling and if they don't accept, at least you tried. If they blow up? It's tough but fair to recognize that not all friendships last. This person might not be a good fit for your life right now, and that's okay, too. It doesn't mean it's forever. It just means right now you also need to take care of yourself. It's not their fault. It's not your fault. It's just a crappy situation, as Faraday says.