Yea he was also wrong about web apps taking over the desktop. They're not even close and it's 2015. Mobile really put the breaks on that.
Web-based apps are also battling it out on mobile. Lot of apps are just wrappers for accessing web-based content. Performance is the primary obstacle stoping mobile from going completely web-based. Both the new entrants, Tizen and Firefox OS (not to mention Chrome OS) have thrown their weight behind web apps. We consume radio and youtube through web. Its not a stretch to imagine Netflix being accessed primarily through the browser in the future.
The growing SaaS business model is highly favoured to web-based apps. It is taking longer than expected, but the future is generally trending in the direction of web-based apps.
Are you suggesting that it's rare for people to use Outlook or Skype?