Two eyes are not a requirement for depth perception. They help, especially for stuff close to you, but are not absolutely necessary.
Don't take my word for it, close one eye and move your head from side to side and see the 3d jump out at you.
Don't take my word for it, close one eye and move your head from side to side and see the 3d jump out at you.
Speaking as someone who naturally has little to no depth perception (amblyopia affecting my right eye), I still see 3D just fine, catch flying objects (balls, frisbees, etc.) just fine, and am not disabled in any significant way except an inability to see into those magic eye puzzles.
Two eyes give you the ability to detect parallax without moving your head; those of us without binocular vision detect parallax by slight (imperceptible) movements of our head. There are many other useful visual artifacts of our 3D world: closer things are larger than farther things, closer things obscure farther things, and so on. Our brains just construct 3D worlds based on those data rather than the simpler, more reliable stationary parallax detection that you two-eyed folks use.
But the difference between what each eye sees is also an important factor in 3D vision. Movies just make it the only factor, which is probably why they can be disorienting. My guess would be that it's more important for things that are close than things that are far away; something 3 inches from your face appears to be in drastically different positions if you cover alternate eyes, but distant mountains look about the same.