Role playing game and also war/combat games. Eventual they created a elaborate separate history for Starfleet and the Federation, the Klingons, the Romulans, etc.
Their "source books" are online (somewhere), you might find them interesting.
Yep. I also know a good source where you can actually buy a lot of the old sourcebooks, and I'd highly recommend them to you. Drop me a PM. FASA still exists as a gaming company, but not on the same scale they did back then. They had a license from Paramount up until TNG premiered, and only made one TNG supplement (The Officer's Manual). Interestingly, it's probably the one product that deviates the most from what has been established since. Most of their TOS-Movie era stuff was based on a smaller selection of canon material and some of the other tie-ins; the Klingons as described by FASA are based on John Ford's designs. While some of that has been overwritten by later canon, a lot of it fit pretty smoothly into the era it was written for.
The name FASA itself is an in-joke by the company staff. It was based on a Marx Brothers movie set in several fictional countries, and one was called Freedonia. FASA stands for the Freedonian Air and Space Administration.