A personal computer (PC) is a general-purpose computer, whose size, capabilities and original sale price makes it useful for individuals, and which is intended to be operated directly by an end-user with no intervening computer operator.
So defined, smartphones, tablets, laptops and desktops are all PCs. The chromebook, running gentoo linux, was Amazon's best selling computer last Christmas. Probably this Christmas too. I can't think of anything a desktop PC can do that the chromebook can't. Nothing is new, excepting size, speed and portability.