It is a joke to say that it is not a real OS.

But if you want to argue: You could say that a 'real OS' must be 'mostly POSIX-compliant' [1]. That way most other OS (Linux, MacOS, iOS) but not Windows would be included in your definition of a 'real OS' ;-)

[1] https://en.wikipedia.org/wiki/POSIX#Mostly_POSIX-compliant

Windows is mostly posix compliant as it had a POSIX subsystem until 2000, then it had Windows Services for UNIX/Interix and now days has Windows Subsystem for Linux.

I wouldn’t get why POSIX is the only way to design an OS.

It is not.

But that way you could pretend to have an objective definition of the term 'real OS' and exclude Windows while including most other major OS.

It’s not. It’s an API. IBM’s zOS has a POSIX-compliant Unix subsystem and it has absolutely nothing to do with Unix under its hood.

regardless of anything else, windows is older than posix... so posix should arguably be windows compliant :P