I'd just install UFW and either set the default for incoming and outgoing to deny and unblock the game ports manually, or just set incoming to deny and outgoing to allow.

You could pair that with OpenSnitch to see all attempted incoming and outgoing connections and block them by default, and then just allow the ones you want as they happen.

Unattended? I'd use a bios password and disk encryption

Yes the PC will be unattended for many hours at a time.

Check out usbguard, whitelist your own devices, preferably no USB drives.
The ArchWiki has a good article on it. I don't use arch, btw.
Other than that, maybe check every time you get back to the machine that your keyboard still directly connects to the machine, without an intermediate device (yes, even with usbguard), but at that point maybe just always keep your keyboard with yourself because a really motivated attacker could just place some kind of keylogger inside of it.

Maybe also look into hardening your lock screen, or finding a simpler one that's perhaps more security oriented.
Maybe it's not the case anymore, but once it was possible to unlock a locked account by crashing the screen locker. Possibly that's not the case anymore, because I remember having to type loginctl something in a new virtual terminal when my lock screen crashed after an update gone bad, but i wanted to make you aware so you can check if you are affected.

You might find it helpful to look up "Evil Maid Attack" as you will be susceptible to that.