When I run Any% No Telejumping I get a better in-game time than a friend who is also running VVVVVV even though he has a much better Real Time. How can this be? And is there any way to somehow manipulate or decalerate the In-game timer?

It's a bit hard to accurately pin down the reasons for the disparity between IGT and RTA. The game tends to lag by very small amounts ( which varies based on computer hardware to a degree) in rooms where there are moving enemies. The biggest instance of lag varying by machine is probably the tower, which is a huge scrolling entity. This is also not a consistent event. On the same machine, you can record multiple runs of the same length IGT that will vary in RTA. The In game timer is frame accurate, so no matter how much the game lags, the time played in game remains the same. Unfortunately, this is the only way to accurately measure runs, since RTA gives a much more concrete advantage to players with consistent/better computer hardware. The downside is that players with exceptionally laggy computers may have an input advantage over players with faster computers during specifically laggy segments, but this hasn't caused any issues yet. No one's machine is capable of making the game run faster than 29.4fps, so don't be afraid that your computer will make certain tricks impossible, as they are all very achievable at the full frame rate. There are some fringe glitches that allow you to reset the in game timer, but they involve saving and quitting, which doesn't suit the single segment nature of most of the categories.

If your in game time is shorter than another player's, then you performed faster during the frames in which you were allowed to input commands.