Fastest- drill it out and replace the lock.
Wiggle the key every which way until it catches just right and works
Pick the lock
Slowest-Find the right key

You didn't specify which game but it sounds like it doesn't have exposed screws on the lock's mounting plate... If they're there you can unscrew them to get the head open, might need a security torx bit or a pair of pliers.

Yeah, drill it out.

Try pushing down a little on the backglass bottom trim piece. It may fit tight and it could be putting pressure on the top latch. I have a game that is snug, and if you push down on the backglass, the key will turn.

I use a 1/8 to start, then 1/4 and go up until lock turns

Or use the brute method, start with a 3/8 and hope it does it. Depends on cheapness if lock.

I just had to drill out a lock on a recent game purchase. I’m sure there’s a more refined/better/proper way, but I used a rather large bit, and drilled along the top and bottom of the keyhole (since it was double bitted). Let the drill do the work, and don’t push too hard or torque to fast. I broke the drill bit in the lock and it took way too much effort to pull it out. What a pain that was.

Go slow and steady, checking often if you can turn the lock with a large flathead screwdriver. Since you’re mangling the brass lock springs, you might need to crank on the screw driver kinda hard to get it to turn.

It’s a bit of a pain, but it’ll work. Good luck.