Prince of Persia came out in 1989, while Flashback arrived in 1992. In the late 80s and early 90s, pc video game tech was evolving at a breakneck pace, a 3-year gap was an eternity. Prince of Persia ran quite well on an 8-bit XT, Flashback needed a 16-bit 286. They are basically from a different era, and Flashback was surely inspired by PoP.
My family's first computer in the 80s was an Amstrad PC1512 (an IBM XT clone). We received 4 nice colorful system floppies with it, and it included a GEM Desktop. I remember sometimes logging into GEM, because it looked awesome, but we never had a single program to run on it, so it was practically useless. https://www.youtube.com/watch?v=DlUTzydzLVI
All these poor agents complaining about amnesia remind me of the movie Memento. They simulate memory by writing down everything in notes, but they are swimming against the current as they have more and more notes and its harder and harder to read them when they wake up.
The article specifically mentions that the weight loss was not enough to explain the effect on the migraine:
"Importantly, while participants’ body mass index declined slightly (from 34.01 to 33.65), this change was not statistically significant. An analysis of covariance confirmed that BMI reduction had no effect on headache frequency, strengthening the hypothesis that pressure modulation, not weight loss, drives the benefit."