ROTT is definitely deserving of its cult classic status.
First and foremost, ROTT is an extremely fun game. It's a straightforward first-person shooter with a lot going for it. Many of its weapons are very original and generally fun to use. Humorous touches are everywhere, especially in the sound effects. The game's 40 or so levels are usually longer than those in most other first-person shooters released in the early '90s. The music, while not always completely fitting, is well composed. I have not had a chance to try out the multiplayer mode, but with the wealth of game types and levels available to choose from, I'm sure it's a blast. Plus, there's just something about this game that makes it terribly addictive...
The ROTT engine can best be described as a mix of Wolfenstein and Doom, with some strange results. While the levels are more interesting and memorable than those in Wolfenstein, they're a lot less interesting and memorable than those in Doom. "Level" would be a better description for these than "area" or "place". On the other hand, they do play pretty well. The color pallette is pretty drab, and the game doesn't include a huge number of textures. Also, some of the enemies are pretty easy, while some are much too tough (for example, the grenade-throwing, machine gun-toting officers who can take 10 times the damage of most other enemies). While there are a large number of weapons at your disposal, you'll end up using the dull machine gun most of the time because of its unlimited ammunition capacity. Too bad.
The Bottom Line
Most people have forgotten about Rise of the Triad, which is a shame, because it's so much fun to play. It's not Doom, but it's almost as addictive. The shareware version is available all over the web- give it a shot.