I think that "the PC is doomed" is a dumb statement. My main issue is with using the PC acronym. Really, all these new small-form-factor devices are also PCs. They are little "personal" computers that perform certain tasks. Sure, the tablets and smartphones aren't good at modeling and rendering 3D animations or what-have-you, so people don't try to use them for that.
The "PC" as we currently refer to it, has already evolved from the original. Its components have seen improvements in technology and a reduction in size. One day we'll be able to have all the power we need in something as small as a cell phone, but at that point, that little device is now our PC. The "PC" is not doomed, it is just evolving.