Dang, I think I recognize that video!
The indexer in that video is driven with a servo, but initially it had a NEMA34 stepper of 640oz-in which was adequate for holding the workpiece with a 3.6 to 1 reduction.
Yes, if you only need to rotate the workpiece for the purpose of engraving, then a stepper would be fine. I would suggest a microsteeping drive and gear it down a lot via a wide timing belt with an idler or other method for tensioning the belt, which has to be very tight.
Keep in mind that in this situation, the belt stiffness and the motor holding power alone is going to provide the rigidity.
What is it you are making?