I thought these bolt to the bed rotating chuck things usually came with a worm drive and an index wheel/pin.
Sticking a stepper in place of the index handle is a CNC conversion.
Replacing the worm wheel with a toothed pulley sounds like a Chinese CNC conversion. More for selling than using.
Maybe you want to engrave toothpicks and this is exactly what you need.
Alternatively, maybe if you bought it as an incomplete conversion, played with it, decided what resolution your usage required, replaced their timing pulley with a nice anti-backlash worm from HPC gears, tried it with the stepper then replaced the stepper with one of those singleton servo drives doing the rounds on eBay.
That could work.