I haven't run the numbers, but a quick look at typical delta-V budgets [1] (which calculate atmospheric losses as 1.5 to 2 km/s of delta-v), if one could accelerate something fast enough that it escapes most of Earth's atmosphere (and only then burn for orbital velocity), you'd be saving ~17 to 20% on the delta-v requirements. Due to the nature of the Tsiolkovsky equation, that could be a very substantial saving.
That said, I'm also wondering why a centrifuge would be better than say, some kind of low pressure tube / rail, but I'm sure these guys have done their maths and believe in it.
We can build electronic components that are rated for 100000 g's. I think craft that can withstand 10's of g's are within our capability to build. Why not make the circle the size of the LHC? Why not larger?
That's ~1000mph less delta-v needed to reach orbit. But note that the air is also moving in the same rotating frame, so there is no difference in air resistance upon exit from the launcher whether you are going east or west.
[1] https://en.wikipedia.org/wiki/Apple_Park
[2] https://en.wikipedia.org/wiki/Orbital_speed