Welcome to the ergosphere.
"Time clearly isn't a dimension."
What do you mean by "dimension"? If you beg the question and define "dimension" in such a way that only the three, extant spatial dimensions can satisfy it, then of course you're correct. But then we already know that time and any extra dimensions are not a spatial dimensions of the sort we see around us - at least, not at temperatures we can survive in.
But if you define dimension as an "independent" variable necessary to describe your position, then time is a dimension. (And, potentially, so too is electric charge.)