Interesting detail I didn't know about, and different to my initial interpretation too.
It doesn't seem too unreasonable to call the program counter, memory registers, etc. "special registers" since they have specific functions beyond simply storing data. Therefore I could imagine calling the aggregate of such registers in a CPU a "special register group". Perhaps those still using the term are following this line of thought.
In that they're not the GPRs (General Purpose Registers) this kinda sorta makes sense. Mostly the problem is that this terminology isn't actually used this way. Notice how the CPU (which we're thinking of as one small component of e.g. a laptop or phone, but the originators were imagining a furniture sized piece of equipment which is responsible for the actual computing) is supposed to be comprised of these particular elements but not GPRs, not an FPU, or an MMU, or any other elements which are in fact typical today.
So this sort of "quiz" is bogus because it's basically checking whether you've rote memorized some particular words. People who know how a CPU works are confused and likely don't pass, those who've memorized the words but lack all understanding pass. This is not a useful education.
This was my thought as well. Any sufficiently complex modern CPU contains some register that it expects some bit to be set in to enable something like a powersaving mode with an interrupt mask in the lower bits to turn it off. Or something equally esoteric, but purposeful once you consider the application.
My recollection is that even the Atmega 8-bit microcontrollers have tons of special register groups around timers and interrupts.
Given the relative scarcity of "general purpose" registers on x86 32-bit CPUs, you could actually argue those are the special purpose registers.
> My recollection is that even the Atmega 8-bit microcontrollers have tons of special register groups around timers and interrupts.
Not precisely. AVR, like most embedded architectures, has a bunch of I/O registers which control CPU and peripheral behavior - but those are distinct from the CPU's general-purpose registers. The I/O registers exist in the same address space as main memory, and can only be accessed as memory. You can write an instruction like "increment general-purpose register R3", but you can't use that same syntax for e.g. "increment the UART baud rate register"; you have to load a value from that register to a GPR, increment it there, and store it back to the I/O register.
AVR is a bit weird in that the CPU's general-purpose registers are also mapped to main memory and can be accessed as if they were memory - but that functionality is rarely used in practice.
Getting back to your original point, x86 does have special-purpose registers - lots of them, in fact. They're accessed using the privileged rdmsr/wrmsr instructions.
The definition doesn't mention that there are any other kinds of registers other than special register groups: it asserts either that there exist groups of nothing but special registers, or else that there exist nothing but special groups of registers.
"special" is meaningless without a the presence of contrasting subjects that are "ordinary" or "regular".
E.g, "The human hands have two special finger groups".
It doesn't seem too unreasonable to call the program counter, memory registers, etc. "special registers" since they have specific functions beyond simply storing data. Therefore I could imagine calling the aggregate of such registers in a CPU a "special register group". Perhaps those still using the term are following this line of thought.