So I just beat the 4th place time in real time, but not in game time. It says I'll be in 5th after it's verified. So does game time matter more than real time? Does real time even matter at all?

The thing is that you beat the actual time he had, but not the one he submitted to the leaderboards.
Since he submitted it before milliseconds were added, his time counts as a 1:52 flat, rather than the actual 1:52.8 or whatever.
Hopefully some very patient moderator will go through the times and edit the submissions with the proper milliseconds

Ahh gotcha. So RTA is what counts then?

Yes, that should be the case

Cute profile pic! @TheCompleteJerk