360 Extender for Vista requires XBL connection?
For the length of the beta program the Xbox 360 must have access to Xbox Live. This is typically accomplished by connecting your Xbox360 to your home network such that the Xbox360 has Internet access.
Presumably, Microsoft will drop this un-necessary restriction in the final Vista WMC release. As Andy points out, the reason you have a TV is so that you have something to do when your internet goes down.