I presume you mean the "red lollipops" or
Gymnocalycium cv. 'Hibotan' Doug?
http://www.desert-tropicals.com/Plants/ ... botan.html
The reason for grafting this plant is it is deficient in chlorophyll and relies on the photosynthesis of the green stock to keep it alive. The plant was discovered as a tiny seedling a few days old in a seed pan of normal seedlings in Japan and seedling grafted at around match head size before it died, because obviously it was not able to produce it's own chlorophyll. The Japanese just love these weirdies, just as they like to produce bizaar goldfish. There are new many versions of this plant from yellow to red and also brown or striped.
The reason for grafting normal cacti is if you wish to push them on faster because many grow much faster on a graft, they are usually grafted on some form of
Cereus. This is often used as a means of rapid propagation, the plant being pushed on then beheaded leaving part of the scion on the stock which then produces numerous offsets (like your red plant) that can be in turn grafted. Using these means the Japanese and the Dutch can soon produce thousands of plants from just a few originals.
DaveW