> refers to these A, B, C as 'registers'
No, A, B and C are called "instruction field", not "register". The registers are referenced in the text like e.g. "R(A)" meaning "the register signified by instruction field A". E.g. the instruction "MOVE A B" is described as "R(A) := R(B)". Each register carries a Lua value. The registers are not part of the instructions, but part of the activation record, which is allocated when Lua enters a function.
Will make it more obvious that these registers are part of the instruction itself as it may confuse people that are familiar with more traditional VMs.