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I'm not familiar with the game but from your description the way the game works doesn't match up with what is understood how general relativity works. GR is conceptualised with spacetime diagrams: time is orthogonal to space. A body in it has to move in either one axis, or a combination of the two. Assuming no acceleration or gravity present, a body moves in a straight line. If standing still (own reference frame) the body moves 100% straight along the time axis. Special relativity tells us max speed you can measure is the speed of light: in that case it moves at an angle that equates to the least amount of time component and maximum component for space. Effectively light would experience no time. The faster you move the less of a time component you express in this diagram. Now, as for gravity and acceleration (the effect of either would be same) this would be expressed as curves on the diagram. These curves would represent the curved geometry of space due to the presence of mass for instance and the implications are that what we think of moving 'straight' is subjected to curving of space due to gravity. Our timeline is moving us straight but earths gravity is making it curved, bending it towards it with us following it. With blackholes this obviously is taken to the extreme. Hopefully this makes a bit of sense.
That's fair. (https://youtu.be/p3NS65DX8DY) It's a fairly good VR game that has a normal PC / console experience as well. I think the implication is the person's in a simulation. (https://steamcommunity.com/app/322500/discussions/0/412449508275508499/?ctp=2)
But it's more about the concept of what if that effect occurred in our natural real world. Ie. Time only moves when you move becomes literal, in the way it's depicted in the game.
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.