Is the MTOW determined by the wheel maximum supported weight?
Boeing1[pdf] specs for 777-300ER:


Max taxi weight: 777,000 lbs (352,442 kg)
Max take off weight: 775,000 lbs (351,535 kg)
Max landing weight: 554,000 lbs (251,290 kg)


Bridgestone2 specs for approved tires: 


Main: 66,500 lbs (30,264 kg) x 12 = 798,000 lbs (361,967 kg)
Nose: 44,500 lbs (20,185 kg) x 2 = 89,000 lbs (40,370 kg)
Total tire rated load = 887,000 lbs (402,337 kg)


So at taxi weight on all 3 gear there's roughly a 110,000 lbs / 50,000 kg margin (about 14%).

At max landing weight, main gear only, there's a 244,000 lbs / 110,677 kg margin (44%).

At MTOW there's about a 112,000 lbs / 51,000 kg margin (14%) on all gear, but only a 23,000 lbs / 10,400 kg (3%) margin after nose gear lift off.

But, when the nose gear lifts off the ground the wings are supporting nearly all of the weight. Their numbers are pretty close to what the manufacturers list. I think you're just not accounting for the nose gear at takeoff and the weight difference at landing. 

As far as Is the MTOW determined by the wheel maximum supported weight? It's the other way around. The MTOW determines how many tires of what weight rating are needed. 



A more important tire consideration is speed. The tires are rated at 204 kt. This paper gives an example of a 747 at 825,000 lb there is a weight margin of 30,000 lb. But liftoff speed is 199 kt, so there's only a 5 kt speed margin.