Legless pilots can handle more Gs than their legged bretherin. When gravity forces blood from the brain to lower extremities, it causes the pilot to black out. But if you have no legs to force blood to, more blood can stay in the brain, and it's easier for the heart to pump blood back to the brain.
Their legs were probably voluntarily amputated as these are all trained pilots. Their futuristic society allows for prosthetics that allows them to walk and run normally so there's no loss in performing these amputations.
Well, my mind is officially blown. I think this is something Nintendo has moved away from in subsequent StarFox games, but I could be wrong. We need a brand-new entry to see if Nintendo will continue this idea!