How some android phone supports 4k video capture and playback while some pc doesn't.? I just heard of the Snapdragon 805 specs and i was astonished to see that it supports 4K Video capture and playback, then came to know that some Sony Smartphones already supports 4K Video capture and playback and it has it the market already.

My PC, an Intel Core 2 Quad Q6600 with 6GB DDR3 RAM and an NVIDIA 9500GT 1GB DDR2  doesn't support 4K Video playback (captured in RED).

Does it mean that those Smartphones that does support 4K Video playback is actually faster and more efficient than my PC if not, how do they do that.?
Most smartphones have dedicated video encode and decode hardware. It's specifically designed for that task, and it has a fast connection to the memory, and often the decoded video frames can be accessed directly by the compositor hardware so they don't have to be copied (or blitted) into the framebuffer. You wouldn't be surprised that a handheld digital video camera can do 4k video capture: it's specifically designed for that purpose. Your smartphone works the same way.

Most PCs don't have this special hardware, so they have to do video encode and decode with software, on the CPU, or with a special compute shader on the GPU. Either way, that's always going to be slower and less power-efficient than having special-purpose hardware.