What’s interesting to me is that this result shares something with the relativistic theory of gravity:
That is, that gravity is a side-effect of the fact that time moves more slowly closer to centers of mass, which causes the velocity vector of an object moving in space to turn in the direction of the time-speed gradient in space.
This is misleading / incomplete. Curviture in the time dimension is not enough to explain gravity. Gravity is caused by curviture in spacetime (4D). It's definitely not intuitive to think about the time dimension (and so makes for a good youtube video), but this "theory" you're talking about isn't anything that wasn't already known when GR was first introduce.
I'm not sure if you just meant GR and "accounts for some of gravity", but it's a common mistake I've seen people make after some youtube videos on the subject.
That is, that gravity is a side-effect of the fact that time moves more slowly closer to centers of mass, which causes the velocity vector of an object moving in space to turn in the direction of the time-speed gradient in space.