There is also the technicallity where the runs in the time attack give the player all the weapons instead of having what weapons you earned... Thus would be another reason why it would be a separate category...
It is a separate category. What they are talking about is the time that shows up in the game list page (each game only lists one time on that page, which is the shortest time of any run on the actual game page).
Which that is funny, because the current fastest
Castlevania: Legacy of Darkness run is (N/A). Wow, I'm so fast, I'm not able to be timed!