I don't think the spindle needs to be a servo. The lathe in the video has an induction motor driven by a VFD. But the spindle have an encoder with hall, same as mine. He uses LinuxCNC though.
https://youtu.be/z6dK41_usfQ?t=281
As i said you need a way to use your spindle as movement and not speed. Don't believe that worth to try with encoders e.t.c
To do something like that with encoder, you need to have a high resolution encoder not just a hal to know where exactly is the spindle. That info need to know mach4 and use is as an Axis ( A, C e.tc.) or have some kind script/plugin to use that info when you want.
If is possible, yes i believe it is, if it worth it, i think not.
The video is turn cutting with rpm sensing and the 1st video was face cutting like a mill.
Ofc someone maybe know more..