I don't think that's true.
From what I understand, yes, you will need a wireless router for the chromecast, but your desktop could be connected to a wired port on the router.
I'm pretty sure that the way all these various wireless boxes work (roku, printers, etc), is that they communicate back to the router. They don't communicate directly with your computer. Though you can make your computer a wireless 'hot spot', but that isn't a requirement if you have a wireless router.
Someone correct me if I'm wrong, I'm going on general knowledge here, never played with the chromecast itself.
-ERD50