I think along the same lines as Jay. What I link most about vinyl is the ease with which the music flows. The continuous waveform vs small discrete block, even very small closely spaced one seems to be the key.
In the past month or so I have been listening primarily to vinyl. Several interesting observations. The first is that I can play records for hours and an nearly always surprised when the side ends. I find I don't want the music to stop. I do find that when listening to digital that I find myself thinking that the CD has gone on for far too long. Perhaps this is becuase of the length of some CD's but I think it's related to fatigue.
Secondly is the foot tapping/knee bouncing effect. While this is perhaps an overused/misused term, I find it applies very much to my physical and mental state while spinning vinyl. When I attend live performances my leg will start bouncing with the tune. Enough so that my wife will tell me I'm shaking the seats.

I told her it used to happen all the time when I was younger when listening to music but rarely now. Since I have been playing mostly vinyl lately I have noticed my stupid leg bouncing along with the tune. Not a conscious act but it certainly caused me to think about the why.
Another side effect of vinyl, solid state electronics seem to sound much better with a vinyl front end than with a digital front end. I suspect this has to do with the fact that a good SS amp is faithfully amplifying all the digital artifacts in the signal. Perhaps this is part of the reason why tube electronics are enjoyed by so many folks. Not sure, but possible.
Mike