You can call the 64 bit architecture x64 all you like, but it's still using the x86 instruction set and it's frequently referred to as x86-64, so naming that 32 bit only folder "... (x86)" will just make things more confusing than they should be.
It'll be interesting to see what Microsoft will do if Windows on ARM actually takes off. As far as I know, the current translation layer can't execute amd64 on ARM, only x86. Will we see Program Files, Program Files (x64) and Program File (x86)? It would make sense; have the redirection system ready to go and the naming scheme would also make perfect sense. ARM doesn't need a special 32-bit folder because there's no notable 32-bit vs 64-bit clash; nobody is migrating upgrading their Windows CE device to Windows 11, after all.
https://stackoverflow.com/questions/12427245/installing-in-p...
- "C:\Program Files" <- ARM64 programs go here, as do x64 programs! - "C:\Program Files (Arm)" <- ARM32 programs go here - "C:\Program Files (x86)" <- x86 programs go here
I'm not sure how things like "Common Files" work in C:\program files, unless they made mixing arm64 dlls with x64 exes and vice versa just work. Which they probably did. I'm guessing they did not want another WOW version, since it was already bad enough to have to ship 3 different copies of certain system components, and they did not want to need to include a 4th copy, especially as ARM devices are often a bit light on storage space.