This is a pretty dense read.

My summary (and I’d appreciate correction from those who follow this more closely):

There is a set of problems where the runtime complexity increase exponentially as the problem size increases on classical computers.

If you can show you have a device where the time complexity only increases linearly and you are faster in clock time then you have shown that your device is superior to classical computing.

Here Google chooses a problem and shows that their 9 qbit quantum device (which they developed) shows exponential speed up between 5 and 9 qbits.

They project that speed up and error rates forward and find it should achieve quantum supremacy at 50 qbits.

(At least that’s my reading. Corrections and expansion very welcome)