But people DON'T prefer the sound of vinyl to CD! Only weirdos that visit sites like this do, and not even all of them! Heh! So maybe it should be called "Why Do Some People…" instead. Nitpicking maybe, but to generalize with a word like "people" would lead one to the obvious conclusion that vinyl lovers are a tiny minority and that MOST people prefer the sound of digital audio.
I don't think vinyl as a storage medium has any scientific advantages at all if you assume that the goal is to reproduce a signal with as little change as possible. It has increased noise, limited playing time, limited frequency response, requires pre and post equalization, surface is susceptible to dust, poor crosstalk between channels, tracking distortion, requires careful setup, calibration and maintenance etc.
For those who like it, the list of "bad stuff" doesn't necessarily matter in the listening, however. There's many other factors at work. The analog\vinyl domain might have more distortion involved but this can be experienced as a positive enhancement rather than a negative one. We just simply like the non-linearities. I suspect bass register resonances in a vinyl system can impart a thickening effect to the sound which can sound good. Perhaps as in a guitar, if there is just enough acoustic feedback through the system it can sound richer. It could be called coloration rather than distortion since it is more subtle than outright fuzziness.
Other factors might be based on the age of the recording. Older recordings made before recording equipment became available to the mass market meant that those making them were highly trained professionals. Older equipment may have imparted a coloration that sounds good. There's tons of factors besides vinyl as a medium. I'd say that a better argument could be made about the superiority of analog TAPE rather than vinyl records. By itself vinyl is a clear loser, but there's so many other factors tied in with it that this is overridden. But the majority of regular people only cared about pops and crackles, and once digital made those go away they were sold. They don't care about DVD-A or SACD either because it's just another more expensive CD with an already-solved problem on it.
Other non-audio pro-vinyl factors would be nostalgia, smell, size and tactile quality.