I think Lightning Blue is correct that the slot for the Broadcom card is usually not present, unless you opted for the card from the factory. It's probably possible to add the slot, if you know what you're doing (people did this to add the missing WWAN slot to the Mini 9).
A half-height Broadcom card will/should/may work in place of the WiFi card. You'd lose the builtin Wifi, so you'd need a USB WiFi adaptor.
I see you asked about a game in your initial post. The Broadcom card will NOT help 2D or 3D gaming at ALL. It's just decodes video.
There's no way to improve the Mini 1012's 3D gaming ability. Better 3D gaming requires a better netbook, like one based on the ION platform. I expect Dell's larger "netbooks", like the 11z and M101z offer improved gaming performance, too, but still not great. The Alienware m11x (especially the newer Core iX ones) should offer good gaming performance, but the m11x ain't cheap.