Yes, it is a real game. Back when Trek was really popular people did actually play it. A digital version would be great... would be a good time killer while waiting for the queues to pop.
Heck, I'd even settle for regular chess with Fed and Klink ships as pieces. Surely that wouldn't be so hard to program.
Mini games like chess and some of the others could almost addictive. People will play them over and over because they are a lot of fun. You're doing the same thing but each game is different, because of the opponent. So they don't feel as repetitious, this game needs is more diversity.
How about Klingon Arm-Wrestling. It seems to be similar to regular arm wrestling except that there are daggers on the table.
You could probably do a game like that pretty easy. Just press away from the dagger or your side of the table. Then let a cast bar fill up and rapidly push a button to keep the energy up. If you let the bar go to high you would lose fast and get slammed. If you didn't let it get high enough your opponent would slowly overpower you.