If gravity wasn't self interacting it wouldn't follow the shortest path that gravity itself creates. Light does follow this path. Gravity would move in different directions and at different velocities to light across the universe which is full of gravitational field if it wasn't self interacting. We have seen zero evidence that gravity does propagate differently to light. In fact ligo and other gravity experiments have only confirmed it's the same.
So gravity is almost certainly self interacting. What does this mean? Well it wouldn't change much at small scales. There's not enough effect at say planetary scales to really notice. But what happens when you have a field self interacting across vast distances and involving vast galaxy sized masses? Well your link looks at this and yes it matches some of the anomaly's we are at large scale.
It's a good theory and I suspect despite being hard to argue against it will face opposition since it means a lot of scientists were chasing a dead end.