It seems that the hyped drop-in/drop-out co-op multiplayer for the PC version of Star Trek: The Video Game is simply not working.
According to the official Twitter "We are aware that some users run into problems starting a co-op game on PC & others are having no issues at all. We are looking into this!"for the game:
Later, the feed responded to a user's "@unfairco Though only a fraction of PC users are having problems, we are working to determine the issue. Please PM with further concerns!",