Here's the part where they explain the theoretical solution

Under Oppenheim's theory, however, space-time wouldn't just be smooth, it would become sort of wobbly and unpredictable.

Here's where it becomes testable. This wobbliness would result in fluctuations of measurable properties that are larger than the fluctuations predicted by quantum theory.

With the right experiment, physicists could look for those fluctuations.

We have shown that if space-time doesn't have a quantum nature, then there must be random fluctuations in the curvature of space-time which have a particular signature that can be verified experimentally," says physicist Zach Weller-Davies of University College London.

"In both quantum gravity and classical gravity, space-time must be undergoing violent and random fluctuations all around us, but on a scale which we haven't yet been able to detect. But if space-time is classical, the fluctuations have to be larger than a certain scale, and this scale can be determined by another experiment where we test how long we can put a heavy atom in superposition of being in two different locations."

I think they don't really do a good job of explaining it, so if anyone here knows more about it, please share!