I have dubious depth perception; two modestly nearsighted eyes. I just took your challenge. I did it perfectly, first time. That's probably because my brain's depth perception mechanisms are used to adding in more cues than brains that can lean on perfect binocular vision do.
People tend to get really romantic about how brains work, so I should probably make something clear. When I say that my brain is more used to integrating multiple other environmental clues to get depth perception than brains with perfect stereoscopic vision, that's actually a bad thing. The resulting depth perception is clearly worse than good stereoscopic vision. I am lucky in that if I wear glasses, which I do not routinely, I can get true stereoscopic vision back; I do not lack the brain mechanisms entirely as some people with bad vision do. And that's clearly better. My brain is better adapted to degraded input, but it remains degraded input. Brains prefer stereoscopic vision when available because they naturally gravitate to the best sources of data.
Rolling back around to my main point, depth perception is a great deal more complicated than most people give it credit for. There's really two distinct depth perceptions, one using stereoscopic vision that only works out to a few tens of feet regardless of how good your vision, and one that works on the rest of the world using motion and occlusion cues and a variety of other things. These flashing pictures manage to fire some of my depth perception based on motion cues, but completely lack the precise depth perception I get from stereoscopic vision. There's really no such thing as a monolithic "depth perception", it's a lot of things that get integrated in the brain.