I found a video on YouTube of animals drifting off and trying to stay awake (by jerking their heads etc. like humans do). Why do they do this instead of just letting themselves fall asleep?
Cat (and other animal) behavior is affected by many, sometimes conflicting, motivations. You can see the same behavior in people when they want to stay awake for some reason but are very short of sleep; when they start to fall asleep their head drops and they then snap their head up and attempt to stay awake again.
Cats prefer to sleep in locations they consider secure; if for some reason they are in a location where they feel threatened or can see possible prey, they wish to stay awake but if they need sleep they display this behavior. I have noticed this sort of falling asleep/trying to stay awake behavior is more common in kittens than in adult cats.
By the way, your example video link is no longer working, but I found another one at https://www.youtube.com/watch?v=2CNd6OGdMO8.