When people say "space time," it sounds like it is.
I think of "dimension" as like a parallel universe type of thing. Here we are in the universe. But, if you saw the show "Sabrina, the Teenage Witch," when Sabrina would go inside of her mirror, and everything would be opposite of the reality when she was living the moments inside the mirror, the inside the mirror universe would be like the parallel universe to the real universe that we are in. Which, for those who are religious, is different from the "physical / spiritual" difference. I think of that as a different realm or part of the same universe. That's how I think of it.
If time is a thing in itself, separate from the universe, then it might very well be a different dimension. Time counts events chronologically, so if there is no universe, there are no events to count the length of what we call "time" to see how long they lasted. But, time would still go on, in the form of eternity. But, if time is only able to exist if something is there to measure time, like how 88 days on earth is one year on Mercury, or like how ten hours on earth is one day on Jupiter, then it's not a different dimension. As far as I think of it.
So, I don't know for sure, but those are possibilities of what might define it one way or the other.