Loop Quantum Gravity (LQG) is an old idea - it is the main competitor of String Theory. I have not read the paper that is in their reference list, but the Science Daily article just gave an overview of LQG. So inasmuch as it’s just talking about LQG, I guess there is a breakthrough, but it’s an old breakthrough.
Is there any connection between the quantization of space in in quantum gravity and a fundamental length scale to the universe?
In LQG, there is no such thing as lengths smaller than some minimum length scale (about the Planck length). Is this what you mean by a “fundamental length scale”?