I think "modern" computing is a better term than "real" computing for what he means, but it's merely presumptuous of a definition, it's nowhere as extreme as calling a table a chair. I'd suggest not letting a definition poison your mind too much as the post is interesting if you can get past the tone.
Nah, only historically. Yes, "8-bit" refers to the ALU. Back in the day, 16-bit was similar. But even then it was muddy, because when talking about operating systems like Unix or NT the key question about bitness would be in the context of a 32-bit flat addressing model, not really the data width.
By the time the 64-bit era rolled around, the "64-bits" definitely referred to address space.. The original Pentium had a 64-bit data path and had instructions (MMX, eg PADDQ) that could operate on 64-bit numbers - no one would call it 64-bit. By the early 2000s with the big push to mainstreaming 64-bit, it was all breaking out of the 4GB address space limitation - not the width of data.
> define the bitness of CPUs by their capacity to add numbers in one go
This is nebulous and therefore troublesome to define. Are we talking about the ISA or the internal circuitry (ALU and/or data path)? Is the 68000 a 16-bit or 32-bit CPU?
We're ~20 years down the line and none of these "64-bit" processors support 64-bit addressing yet. Most support up to 48-bits of addressing, with some newer intel chips supporting 57-bit addresses with 5-level paging.
I always took the bit-ness of the processor to refer to the data bus size between the cpu and main memory, aka, the size of a machine word.
By that definition, the Z80 would be a 4-bit CPU ;)
https://www.righto.com/2013/09/the-z-80-has-4-bit-alu-heres-...
...but if you take the data bus width, then the 8088 would be an 8-bit CPU, which isn't quite right either...
But you also can't take the address bus width, because modern "64-bit" CPUs can't actually address 64 bits of physical memory...
I think it's best to treat the 'bit-ness' of a CPU or computer system purely as a marketing term.