Everything you said is correct except for that part - Skype is available for other platforms as well - including Mac OSX, Linux (but the Linux version is always way behind), Windows Mobile, Smart Phone, Nokia N800/N810 and WiFi phones with integrated Skype and standard cordless phones with integrated Skype. So WebTV users that don't want to buy a PC could as well buy a phone to use Skype. In some countries there is also a Skype phone available, called "3 Skype phone".
EDIT: On this Skype download page: Download Skype for Windows you can see a rather complete list of links with further information on all the platforms that Skype supports on the right hand side.
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