Do you have math for it? Because without math there is no model, and certainly no theory -only hypothesis.
Einstein modeled gravity and time dilation as curvature in space not because he believed space existentially curved, but because it is a beautifully elegant and effective way to describe the behavior we observe.
In fact, under Einstein's theory, gravity is indeed not a force. General relativity describes gravity as objects traveling along geodesics in curved spacetime, meaning gravity is a virtual force, or a phenomenon that looks like a force in one context but is not in the system as a whole.
And no, we do not expect space to "flatten out" across large distances. In fact, modeling gravity as spacial curvature leads us to the exact opposite conclusion. We expect the curvature to become less influential asymptotically, never reaching 0. Of course, gravity also has a speed, so what we actually expect is for the wave to travel outward without bound, but I'll leave it at that.
Spacetime is also not a field, it is a pseudo-Riemannian manifold called a Minkowski space. Fields propagate through space.
The most immediate issue I see with that paper's proposition is that it imposes a static reference. Space, under general relativity, has no sense of absolute location -you cannot move through space itself. You can, however, move through space relative to another object. What the paper describes is an aether, where space itself is a physical entity reacting to movement and interacting with objects.
For instance, under this model, time dilation occurs to an object as a result of moving through space. That does not describe what we observe at all. What we observe is a difference between the time experienced by multiple observers moving relative to each other. There is no time dilation without an observer. You can, in fact, travel anywhere in the universe in an arbitrarily short amount of time -but the planet you took off from will only see you moving arbitrarily close to the speed of light. There is no correct frame of reference, there are only different references.
Even if this model had no apparent flaws, I do not see what merit it would have over general relativity. A model is not measured by its existential correctness, as that is not something we can verify -it is measured by its predictive power. Einstein's model has extraordinary predictive power, not only enabling far more accurate modeling of the interaction between spacial bodies and their effect on light, but also paving the way to entirely new concepts whose existence we continue to verify, like gravitational waves. I do not see what this model accomplishes.
