Doom 2016
The game does care about contrast. There is always a dominant color in the environment and the enemies do have contrast in the environment to be easier to distinguish from the background. The environment's saturation is always a bit low to favour more saturated enemies, which emphasizes the action. The textures themselves have good contrast with easy to recognize shapes and colors. This makes it much easier to see grates and openings for example. The game does compromise on dynamic shadows for performance reasons, but the game manages to keep a good perception of depth and a very clean image quality. If you look closely there are many things that don't cast shadows. This isn't an issue in this game because it's a high paced game with bloody action and players wouldn't notice that not everything has shadows. In doom 3 the real-time shadows were very pronounced, but the environments were dark and with narrow spaces. A compromise had to be made.
F.E.A.R. 2 Project Origin
In the first mission of the game the player is about to enter a penthouse. The lighting outside has a blue hue while the lighting on the inside has warmer hues. This creates a strong contrast between cold / outside and warm / inside. The cafeteria to the right is the entrance point and it has lights with a warm color.
When the player reaches a ruined city after a nuclear explosion the same cold x warm contrast. This time around it's dusk and the sunlight is warm, whereas the lights inside the buildings are blue and cold.
Is there a rule for warm x cold contrast? No. It depends on intentions, context, atmosphere, what the developers want to convey. There isn't one single answer.
Sonic Mania
Every background has a lower saturation and brightness that the foreground.
Unreal Tournament - Outpost 23
This map is dominated by white with a few orange details and blue energy light. With a clean environment like this it's easier to spot players.
Note that depth perception is good because there is a good contrast between light and dark.
Bioshock Infinite
https://www.youtube.com/watch?v=7-WH-i2Piy4
In the beginning of the game there is this baptism scene. The place is dominated by lights from candles, which contrast with the blue light where the player has to go. There are multiple techniques in use here: cold x warm lights, a straight path with water, symmetric angels, an arch and characters moving forwards. The choice of colors and the architecture are a matter of style and designer's or director's preference.
Control
The environments in this game have a predominance of concrete and concrete is mostly gray. First they have chosen brutalism as the architecture style for the Old House. Now the reason for presenting clean environments and straight lines is deeply rooted in the game's combat design and physics. The main character has the ability to toss objects with telekinectic powers. Some enemies do that as well. It was expected that the environments would become cluttered and chaotic with the player having to toss all sorts of objects onto the enemies to kill them. The player can even use their telekinetic powers on the floor and walls to grab pieces of them. The blue health icons, the red hiss, yellow sparks and rockets, all have a very good contrast over the background and even after a heated battle the environment still retains a high contrast ratio.
The Hiss, a supernatural entity which is the game's antagonist force and enemy, does not have a body and its sign is a very strong red light. I have no idea why they've chosen red, but red has the highest contrast possible when placed over clean and gray backgrounds as in the Old House. It could also be noted that the Hiss invades the bodies of all personnel inside the Old House, except for those wearing a protective gear. This would also give another reason for almost all environments to be clean and tidy. The Hiss invasion was unexpected and by being a supernatural force it just took possession of everyone in its way.
Control is also an example of contrast that is not about colors and textures alone, but also metaphorical. The building's structure is made with straight lines, order and logic. The Hiss and also the Mold are entities from another world or dimension which disobey all the order built-in the building's structure. They are chaotic, messy, don't obey to the normal rules that the personal working there would obey to. You can also notice that when Jesse cleans a control point, all the chaotic cubic shapes that the Hiss has placed are undone and the place reverts back to its original orderly structure. We also have a conrtast regarding geometry in this case.