I'm not sure what some of you are seeing on the screen. I just watched this again, on my 61" TV. It's as clear as it can get. The climbing movements look like stop-motion or an animation to me. The legs and arms bend unnaturally as I see it. I would be very surprised to find out that this was a man in a costume. The movements are so exaggerated and unnatural to the way a man would climb, even if he was mimicking Kong himself from the other parts of the film.

Look at how one leg just hangs while the other moves up onto another level and vica-versa. It's as if Kong's climbing leg was being animated while the other one is left to dangle. Plus, Kong does not have the mass of an actual man climbing. If it were a man, you would see more mass and weight as he climbs upward.