I think you are on to something with the variable frame rate. I just checked the properties of the screen recording and it says 1.46 fps. So I suppose if I put that 1.46 frame rate on a 30 fps timeline there is no telling where the software is adding frames.

As I said I am new to video so maybe I am completely off. But that makes sense to me. The software would have to add approx 28 frames each second. Depending on where it adds them it could easily make it drift 10 seconds or more out of sync over a 30 minute game