This is a case where "ox" means any bovine, like in ox-cart -- sorry, I forgot about that. Rather like neat's-foot oil -- neat is an old name for cattle, but is now only used for the foot-oil (used for treating leather).
Likewise the modern townie trend is to call all cattle "cows" -- including, as I once heard said to a child: "Look at that daddy cow". Ugh!
Many of the cattle words had broader, or different meanings in the past. Heifer, for example, used to mean young beast of either sex.
Ox-tail still seems to be allowed (ours come back with the carcase), though I don't know why as it has spinal cord in it. Kidney, heart, lights and liver are definitely OK, but not spleen, guts or blood. Nor brains of course.
I bet cheek would be OK if you minced it fine enough...