I reckon this phenomena could kinda be phrased like this: Moving through space takes up your turns, when you're moving really fast, most of your turns are taken up by moving (so there's less turns left for the operations of ordinary matter, which we use to measure the passage of time, so it seems slower).
Time most certainly is not a dimension (or even very dimension-like, in general) in my opinion. It structures the orderings of events, more like some ultimate process that all other processes are hanging off (are a part of). The complexity in the ordering could be irreducible at any given point, depending what is happening there, and that includes fully non-reversible processes. To me, this is time's arrow.
