Silly people.
I have MKDS, as well as a Mac, and it works just fine, the Nintendo wi-fi. You'll need Airport Extreme or Airport Express, and the encryption must be WEP. If it's WPA, you must switch (temporarily or permanent, it's fine, as long as it is WEP while you're playing).
That USB adapter, though, is only compatible with WinXP. So, if you don't have Airport Extreme/Express, you're out of luck.