For example, it would be difficult to make an instruction like fyl2x or fadd cause a privilege level change. The reason is that floating point instructions are executed on a separate unit (the FPU), with a separate decoder. This unit would not have the means to communicate back information such as "change privilege level" (normally it can only signal floating point exceptions, and other than that its only output is on the floating point registers). It would make more sense to encode the backdoor on an illegal opcode, i.e. an opcode that under normal conditions would generate a UD# exception, but with the correct values in the registers it would trigger some undocumented behavior.
Another question is how to hide this backdoor in the microcode. Presumably, at some point someone might stumble upon the backdoor and ask around about it. If the backdoor depends on some "magic values", it would be relatively easy to spot just by looking at the microcode.
There's also the point that the author mentioned of "fixing" the processor at some point during the production process. I don't think that the author understands the way mass production of microchips works. It's very much not possible to do something like this while keeping the production price on the same level (or someone noticing this extra step in the production process).
All in all, it sounds much easier to find security bugs in other parts of the system.