If I have understood the article correctly one would be able to measure the length of a spaceship relative to the Planck length and deduce velocity, entirely locally (i.e. onboard the spaceship).
This is a fundamental departure from general relativity which says there is no special frame of reference.
There are many attempts to combine these theories into a universal theory (pun intended), but it is hard to check the corner cases where those theories differ. That's one of the reasons we build better and better particle accelerators.
Either way, it doesn't make sense to apply (pure) general relativity to the small scale, nor to apply (pure) quantum theory to the large scale. The physicists know for decades about of that issue and are already taking care of that.
For the most part particle accelerators are not needed to explain quantum gravity, we do use them to find "new physics" but this new physics is more in the lines of the known unknowns.
We also do apply relativity to small scales every day, without relativity muons could not be discovered and without relativity to some extent even large particle accelerators would not "work" because the effects of spatial contractions are pretty important for how we predict and analyse the data coming from particle accelerators especially the "messy kind" like the LHC.
As for the large scale stuff as mentioned earlier quantum gravity is pretty compatible with general relativity in terms of explaining how the universe that we see today looks and works, you can easily explain why and how the moon rotates around the earth, it does rely on a massless spin-2 particle called a graviton which is yet to be "discovered" and it does break if the graviton would have a different spin (for example spin-0 graviton).
So I don't really understand the notion of why people still think that quantum gravity and general relativity aren't compatible to the extent of "what the fuck is going on", which is odd since afterall GR isn't 100% compatible with the Standard Model either, since GR is background independent and does not care about the particular state or shape of space-time while SM does.
Not sure at which point you disagree with my statement, though.
Each theory is useful for various things because each theory provides you with certain tools and perspectives that are useful for performing specific tasks.
At the end every theory is a set of laws and abstractions you use theories to change the perspective of how you look at things but these are often abstracts.
You can look at particles as particles, waves or fields it doesn't change reality but every one of these viewpoints comes with its unique benefits and you can chose between them depending on what benefits you most to for a specific task or a situation.