In short,

To see Requiem is to see yourself, that's why even non-Stand users can see it.

Requiem is being projected by the soul of whoever sees it.

And for us, Requiem is both "Boss's Stand" and "our souls", which means

To Boss, "our souls" are nothing more than "his own Stand".

That is why Boss can manipulate the souls of others as he sees fit.

After becoming Requiem, it can no longer use the KinCri Punch because it lost its physical nature as it gained an abstract self-identity that depends on the ego of every other person, which is "the reflection of another".

Considering Boss's own identity has become disassociated and unstable, it truly is a representation of the mental state he must be in. The emergence of Boss's other personality from the depth of his consciousness has made King Crimson's very existence vague, like a concept so to speak.