If you only define "the computer" as the white box sitting at your desk, your point of view is valid.
Your old computer won't change, you'll always have one because the hardware doesn't evaporate on you even if the OS does go away on you (like many will starting in 2014 when XP support ends and Ballmer's boys quietly "encourage" you to upgrade your old box by letting it get munched by a virus).
Even then you can always load another OS on your old hardware, or you can take the hint and go buy a new small box.
However, what is changing is the "tool" itself -- a lot of other people are choosing to do their computing on alternate instruments instead of the traditional white box, especially to do their casual or entertainment computing.
Xbox, Nintendo, Wii, Roku, tablets, phones -- all of these things do computing tasks as well. And they are getting used more and more because they ride in your pocketbook or your pants or are hooked up to your big screen TV. Many consider these "entertainment" devices in their thinking, but they are really little computers.
So, back to your main point -- death of the computer as you know it.
What will kill off "the PC as you know it" will be the form factor shrink the new technology provides, plus the drastic increase in the horsepower of those little portable devices.
Even Intel thinks the Next Unit of Computing comes in a 4" by 6" by 2" little box (which will get even smaller as time goes on). Go ask Dell how big a computer is (not much bigger, really). HP still makes a few larger boxes, but they are mostly empty air inside at this point.
So, do what I do with the news, jest don't watch it very often.