After reading through the GDD and the others' comments myself I share a few sentiments but enjoy the idea of the game.
The document is a bit more verbose/pitch-like than it is imperative design. It read more like a pitch to a publisher rather than a game dev team oriented graph-and-chart or specific sequence kind of document.
Despite that the approach to the narrative design and interactions of the game as a platformer is intriguing. I had to scroll down a bit myself to piece together it would be a 2D Platformer but I got there eventually.
The protagonist's interactions with characters from each period is also interesting, though I find my suspense of disbelief waning a bit in how solid the narrative cohesion stands. Specifically, if Dr.Rayden is a highly-skilled futuristic scientist might he already know most of the concepts the native denizens of the timelines he visits tell him about? Maybe a side-effect of the time machine makes his memory foggy or fragmented and then each denizen jogs it back up to solve the problems he needs to in order to journey onward through time?
This is still an adventure game I'd play myself; I love Sci-Fi and this theme is an interesting one to explore!