In a very non-technical answer. When I look at things, there is blur, and a lot of distracting light effect, and I doubt this can be replicated on a monitor. I find first person games really, really, fake. No matter how you see it, the main character is frequently seeing like a frog (massive peripherals), an eagle (telescopic vision), a fly (bullet-time), or a combination. The only time the character blinks is at the same time you blink.
That might be unrelated to the plastic look. But I think it's not so unrelated, people want to look like they have amazing supermodel skin, really shiny skin that's been rubbed with oil.
In a technical answer, all I know is it's the lighting. Movies can be tweaked by after-effects, and I stumbled over a WALL-E article about the movie makers spending half their production time to replicate real cameras. That means to make it look real a game developer may need to spend twice as much to finish the movies, and clean up plasticness.
Idk enough to say if this helps in real-time rendering, but I know there's plenty of baked rendering.