What kind of art style is this? I'm currently trying to find a particular methodology with which I can texture the environments in a computer game (stay with me here!). I'm drawn to the clean, low-frequency detailing from a game published in 1995, Delphine's Fade to Black (have skipped to the start of the game here). On the PC this game mixed gouraud-shaded polygons for objects and characters with stark, low-resolution textures for most of the game.
I've always been attracted to low-poly art in CG, and precisionist art in traditional mediums, as seen in the following examples...

Note - hard shadows, distinct blocks of colour with gradients. There are a few games which have borrowed from this style - Ico, Team Fortress 2, Rime (among others) and I think it might work for the game I currently have in mind.
That said - the Fade to Black wall texturing seems to my eyes (despite being a low-res texture map) a little more impressionistic/abstract than Sheeler, Smart et al. Details and folds are hinted at with a simple block of dark green, rust is implied with a couple dabs of brown. In fact, there's a touch of the screaming pope to it, to my eyes:

Obviously Bacon's work is way more detailed and frantic, but I can't help but think that the impressionistic, low frequency detail of the Fade To Black environment texturing has more in common with Bacon than the totally cool, remote Sheeler.
So my question is: Does anybody know of a particular style of art which combines precisionism with elements of impressionism, daubs of paint, implying detail etc.? Does anybody have any examples of this that I could investigate?
In truth, I'm a bit of a traditional art ignoramus, but I think this might be useful research for my project.
What you're talking about isn't just one style or school, but it sounds like you may like works coming from: scuola metafisica, surrealism, American modernism, American realism, expressionism, and symbolism. 

Now, as I said, the characteristics you described don't define any school of fine art in particular, so within those schools there will be works that do and don't fit what you're looking for. 

Definitely check out Egon Schiele and Giorgio de Chirico.