Do any other third-party USB adapters work with the 360, or is it a unique chipset? Just asking because 13,000 Yen seems kind of steep for what it is. :?

Fifty quid seems a bit steep to me too, but I dont have an X box 360. I would assume that unless the socket is different, or the pinout then no.

only alterantive is an Access Point connected to the box with a short cable.

MS are a bit cheeky with the way that their USB devices work. They have a special chipset in them which prevents 3rd party version from being used; its the same with the camera !

I was using a Wifi bridge (WET54G) plugged into to the ethernet port rather than the offical 360 wireless adaptor.

I wouldnt say special chipset, they just only include a driver for their own wireless.  You can use a wireless bridge so it plugs into the ethernet port of the 360 or you could get a second access point and bridge the access points.  I am not sure how that will affect the operation of the access points as accesspoints, ie if they bridge they can only bridge.

I use a Linksys bridge to connect the Xbox in my living room to the network so we can stream media to it and watch in the comfort of our living room.

you can use an access point as a bridge and it still works as as an access point