I don't think about the software installed on that computer at all.
Also: desktop computers, in my opinion, pre-date the "desktop metaphor" and GUI environments.
I kind of doubt that. When the metaphor was introduced by Alan Kay in 1970, there were no desktop computers. If you consider microcomputers the first desktop computers, which you should since their predecessors, minicomputers, were "cabinet" computers, then the Micral N in 1973 would be the first "desktop" computer.
When Alan Kay was working on GUI environments, it was on equipment that pretty much nobody could access, it was very expensive and few units were sold. Still, it's interesting to note that the Altair was not a desktop computer that could literally sit on a desk: it came in a cabinet that was meant to sit on the floor. ;-) The irony!
When Apple released the Macintosh, I believe most people were interacting with desktop computers that lacked a GUI desktop environment. Specifically I was thinking of the IBM PC XT , although, as you note, there was more to the field than just that.