I have that same machine, cabinet, and stool as you have described. From photos that I have seen it appears that these stools all had that same "vinyl" like cover. However if the machine was used a lot, most of the stools have that chipping on the corners from wear and tear. When I got my stool, it was already recovered with fabric (as shown in the link below) and I think I prefer that even though it is not original. I am not too keen on sitting for any length of time on vinyl especially in hot weather.
https://supermomnocape.wordpress.com...t-is-finished/