The huge thing that this article fails to take into account is the frequency of upgrades. Most people are not buying brand new PCs every two years, but almost everyone upgrades their phones that frequently and I'd be willing to bet that tablet upgrades will follow a similar pattern.
So a user who has a Windows Phone and a Windows Tablet will bring in $30 ($15 licensing fee x 2) every two years. If the average PC is upgraded every 4 years then the $60 of revenue for Microsoft that they realize in a 4-year span in this hypothetical post-PC world would end up perfectly matching their average revenue for Windows right now.
Does the average home user buy a full-blown copy of Office? Probably not, but I'm sure that people will be willing to pay a monthly fee to back up their documents or access some sort of Office subscription. Businesses will, of course, get on board with a subscription model too. Or if they're willing to keep paying full price every few years that's just fine as far as Microsoft is concerned as well.
Furthermore, some users will end up with a Windows Phone, a Windows Tablet, AND a Windows PC. That's even more licensing revenue for Microsoft.
$15 sounds scary compared to $60, but only if you think that people will hang onto their phones as long as their PCs. They won't. If all of this plays out as Microsoft hopes then they are going to be just fine.