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You still need a desktop with hardware support and APIs that underpins that.
It's typical of that whole crap around the virtualisation hype when people were saying you don't need operating systems any more. Errrrr, a hypervisor needs hardware support.
He's actually talking about growing maintenance cost on fat desktop. Fat application have a higher maintenance cost because you've got the whole release/update process that's made much easier with web apps.
But sure, you'll still need a "desktop" computer with a web browser to connect to these apps, it's just that instead of using firefox/thunderbird/openoffice/your file browser, most users will use an all-in-one cloud offering (like Google gmail/docs/calendar).
This actually make a LOT of sense for most non-technical entreprise users that usually just use an office suite and some internal apps (that are more and more web-based).
But you'll still need fat client for most resources-heavy apps : programming, cao, photoshop, etc...
I mean it's kind of the same thing as with the commandline interface. In the 80s, it was the only interface everybody used. Now, for 99% of users, it has been replaced with a GUI, but it's still useful for the techies.