The only reason I can think of for that is other ppl are using your wireless, I have never seen any program that will download that much in the background so thats out.
FFXIV from my guess doesnt use much more internet than FFXI.
And I cant see what turning your PC would help appart from sceduled downloads.
As I say the only problem I can think of is unsecured or inadequatly secured wireless so I would get WPA2 setup, unsecured wireless or WEP is like having a huge neon sign saying "COME ONE, COME ALL FREE INTERNET FOR ALL NO CATCH COME GET YOUR FREE INTERNET".
Also you may wanna change the password on the access point if you have the default password still and setting the MAC filter wouldnt hurt either.
Maybe run a virus and spyware scan as well because they could use alot of internet.
FFXI (Long since retired)