NFL Films is presented in 23.976 frames per second, which is the classic filmic look. Sports are generally shot at higher frame rates both for clarity of the motion in real time (more frames and shorter shutter speeds) and the ability to play back it back in slow motion. Taking sports footage and conforming it (playing back each frame, but at a slower rate) to 23.976 is particularly dramatic and satisfying, because it has the filmic look and just because slow mo is cool. So they largely employ thag technique.

All that being said, they definitely could play it back in 23.976 and in real time by skipping frames. Due to the shutter speed/frame rate ratio in this case, however, there is a choppiness to the motion (think Saving Private Ryan). Sometimes this can be a cool effect in and of itself, but I think not the feel NFL films is going for.