Gaming PCs are very often desktops, though I think those tend to be used more like consoles nowadays, not general purpose computers.

My anecdata is that the households I know that have desktops are gamers, yes, but:

- the desktops in question tend to be "exclusively" used by one member of the household

- the desktop owners usually also have a laptop

- the desktop-owning households are well in the minority of households I know