There's a fairly new game out there called Artemis Spaceship Bridge Simulator, and there is a Star Trek (TOS) mod for it.
Basically the game works like this. You start the server, which also serves as the viewscreen. Everybody plays in the same room, and they connect their laptops to it and take on the various bridge stations and you fly the ship around and do battle (with Klingons and Romulans in the mod).
Here's a video
showing off the gameplay.