

Superhot is emulating accelerated thinking. It’s not that time speeds up as you move, but that your thinking speeds up when you don’t.
Plot SPOILER
Given the plot is about an AI slowly hijacking your brain/mind, this makes complete sense.
Physics wise, this is the reverse of what would happen. Hypothetically, if you reduced the speed of light to an extremely low value, the opposite effect would occur. Time would move slower as you moved. Standing still would give maximum apparent time speed, while moving fast would slow your perception. It would also cause significant distortion to your perception, due to length compression. Not to mention how much it would screw up your body (what the hell does blood do, when time is passing slower in your arm than your torso?!?).
A good example of how it might play out can be seen in the bobiverse book series (we are legion, we are Bob). The main character ends up as the AI of a Von neumann probe. He/they spend most time at 1:1 speed (for sanity purposes). They can, however, “frame jack” to massive speeds for short periods. They use this to problem solve, before returning to more normal speeds to enact their solution.