I disagree.
Firstly, let's take care of the notion that in FPS the role of the player is one of a person. The person part in the label refers to the perspective. If you replace every character model in Quake with the model of a rock, it's still an FPS.
Then let's take care of the shooter part, since I assume it's the easiest and least troubling part of the definition. The main thing that distinguishes FS in this part from any token FPS is the key mapping. Instead of having to switch "guns", you have a dedicated key for missiles, as other FPS have for instance for grenades.
Finally, what may be more troubling, from what I sense in Battuta's post, the movement of the player. FS has from what I can tell two things that differ from standard FPS's in this regard.
The player occupies a true 3D space, that is, the battlefield can be regarded as a 3D space, unlike most FPS's where while it's a 3D space, we occupy a limited, almost 2D portion of it. We can argue against this doing a mental modification of another mentioned game, Tribes. Let's suppose that jetpacks have infinite fuel and that while maintaining gravity, we remove the environment, specifically the floor. Is it still an FPS? In my mind, it is, and from here to removing the gravity and altering the jetpacks controls is a very short leap.
The second is that the player's speed is controlled by a gauge that doesn't change instantaneously. This differs from the instantaneous WASD standard that the industry has settled with. We can divide this issue in two parts, the gauge and the time lag between the player input and the desired output. The time lag is easily settled in that there are FPS that implement that kind of time lag to simulate a person stopping to run. The gauge, is a design limitation that some early FPS's share.
To be honest, the entire discussion can be summed up with the phrase, "Descent is a shooter".
P.S.
Genres overlap, I'm not implying that all games that employ a first-person perspective and that are shooters are just FPS. A game can have many genres.