I was really curious about this because the idea is pretty cool. I’d totally buy one if it was for real. I did some research and found this:
Plants of the same botanical genus and species can usually be grafted even though they are a different variety. Plants with the same genus but of a different species often can be grafted. But the result may be weak or short-lived, or they may not unite at all.
Plants of different genera are less successfully grafted, although there are some cases where this is possible. For example, quince, genus Cydonia, may be used as a dwarfing rootstock for pear, genus Pyrus. (University of Missouri)
All of the fruits listed (plums, nectarines, peaches, and apricots) share the genus Prunus, so if you go by my link, it should be possible.