Looks weird, doesn’t it?
According to Tony Byrne, that’s what at least one publication will be using from now on;
Forthwith, the following terms, “web, website, webcast, internet, intranet, the net” shall merit only lower-case treatment.
Now, english class was never a favourite (ahem), but I think I know what a Proper noun/name is, and by that measure, of that list above, “Web” and “Internet” are most definitely proper names and therefore warrant capitalization.
And why pick on the Web when there’s far better demotion fodder around?