Almost inevitably, when a guidebook talks of drop offs on both sides, they are talking about the windows. Since I am afraid of heights, when I was preparing for my first climb up Whitney, I fixated on that. I shouldn't have done so. Assuming no snow/ice, this should not be a problem for most folks. It wasn't a problem for me, and I am more sensitive than most to heights issues. It also wasn't a problem for a close friend of mine who is even more sensitive than me. If you go through first-timer trip reports on this board and the other one, you won't see many folks mentioning it. For most, the windows are simply a nice place to stop and enjoy the view.
If there is snow/ice, then that's a whole different can o' worms, and not just at this location....