I assume his desktop does not have wifi capability in which case it makes perfect sense.
That is absolutely false.You are wrong. If his desktop does not have wifi capability then he could not print via wifi if the printer is set to connect via wifi. Conversely he could not print from his laptop via wifi connection if the printer was set via wired ethernet to connect to the desktop. You can't have it both ways. The only way it would not make sense is if both printer and desktop were wifi capable in which case you would not need a wired ethernet connection. This is what everyone is suggesting he do but maybe he doesn't have wifi on his desktop.
I use the HL-2170W version of this printer so I know what I'm talking about.
Your desktop should be connected to the router by ethernet cable.
Your wireless printer should be connected to your router wirelessly(after you've installed the drivers properly).
Anything you print from your desktop will be sent to the router which will send to the printer.
Your desktop doesn't have to have WiFi...Mine certainly doesn't.
This stuff isn't magic pixie dust folks. I'm not a computer geek by heart(I don't know linux, programming, and I never took a single computer class in my life) and yet I know how to set it up by following simple instructions.