When people say "Linux on the desktop" (assuming they are not being pedants, using it for anything with a Linux kernel that runs on a desktop class machine, e.g. that they'd include Windows if MS replaced the kernel with vmlinux) they don't go for etymological or technical compliance with the term.
They just mean (casually, not as in "real Linux" purity) a family of Linux-derived distros that might even include a company-made desktop environment (e.g. Mint) but do not include Android.
So, phrase-wise this is not as much about having some attributes checked (runs Linux kernel, check, has GNU userland, check, it runs on desktop machines, check), it's more about belonging to a club. Most people saying "Linux on the desktop" don't want to admit Android in that club.
Partly it goes back to the era of the original "Linux on the Desktop" dream 20+ years ago, where the term meant Linux distros taking over from Windows and Mac, and was associated with FOSS, freedom, bazaar style development, community, and so on, winning over proprietary OSes.
FWIW you can run Android on a desktop; you can run ChromeOS too.. those are both linux.
But you also have; GNOME+Linux, KDE+Linux, i3wm/sway+Linux.
Each of those are so wildly different as to be effectively different operating systems; people are not interacting with the kernel directly and normal users are not interacting with the Command-line in an effective way either. (and even if they were the the differences between distros and window managers would make it different enough that it could only be tangially related really).
Yeah, Android isn't a "real linux", but, part of the issue is that nothing is "real linux": it's a choose your own adventure story and that's why most people think we're all stuck-up when they try a distro and we tell them that they used the wrong one or to keep sticking it out.
It's contrived; if Android can do the job of a desktop replacement (which, it can, there are desktop modes), then why isn't it a real linux?