As someone with long industry experience, I share your disbelief. I'd need to see the Fitts tests results for 250ms max delay (<150ms median?) on button state, as long press is also a thing. On touch/trackpads typical double tap rate is 4-5Hz and maximum tap rate is about 10-15Hz, achievable by relatively few. It's notable that you're dealing with a touchscreen here and not a mouse (people are faster at that).
Most premium Android phones in 2016 were 120-30ms motion-photon response time (low to midrange probably hit 250), while iPhones were ~80ms. Haptics add another ~30ms delay. There have been massive improvements since 2016, as it has been a competitive metric, but even with >120Hz screens sub 60ms max true latency is uncommon.
As (actually my long term memory of) the MS video shows faster refresh and lower latency greatly improve smoothness and are useful for moving objects, especially scrolling (though tearing is a real issue). The problem is much more pronounced in VR/MR as eye tracking of diagonal motion is VERY discriminating. That's why they shoot for >240Hz refresh rates. Over 1kHz there doesn't seem to be a lot of improvement (2ms latency) due to a combination of cone/rod/neural filtering.
If you want a very generic worst case latency calculation based on the touch acquisition rate and display refresh rate assuming no position calculation delay it is:
Latency = 2/Ftouch + 2/Fdispl = 2/16Hz + 2/16Hz = 250ms