Not every skill needs a lot of muscular movement. The program is great for visualizing training and techniques on a limited budget (as said earlier). Though nothing replaces actual hands on training the key reason to use VBS2 or 3 is the limited budget. The guy who mentioned his COLT team using it is a good example. Calling for fire, close combat support or close air support is not that much different whether your watching some target take an actual strike or watching a digital target take a digital strike; the procedures and feedback is similar.
At the original question, I would say simulator. Out of all of the FPS games I can quickly think about that comes close to simulator I think of BF1942. Their artillery required adjustments with every shot, there were weak and strong points to vehicles, it did not require you to be a good twitch player to be good at the game and there was a reasonable hit to kill ratio (meaning you couldn't just soak up bullets because). However, it's still an FPS for one main reason, the health bar. Eventually hand grenades could kill a tank wHile in something like ARMA you could try all day but you would just be annoying.
So I think what defines ARMA as a simulator is the realistic weapon feedback with the player as well as the realistic weapon interaction with their targets.
