I don't know how that specific game implements things, but from what I can tell, the camera picks up exposure from two different light probes during that movement. The differences between the two is significant, which is why you are seeing such aggressive exposure changes when moving just a few meters. RT global illumination will help make this transition smoother and more natural, as exposure adjustments would not be bound by the boundaries of those two light probes the camera goes through.
Assuming this is camera location / light probe based exposure adjustment, and not a simple screen space exposure adjustment in regards to where the camera is looking.
You guys do Automatic Exposure based on light probes and not based on what's showing on the actual screen? I have never seen that, I wonder how that works.
Anyway, as for the OP, and although it's already been explained... exposure control is something you can't get rid of, unless you're OK with the games not having anywhere near correct lighting in them (which can still be visually appealing, mind you, just missing
a lot of what would make it realistic).
In many engines, it's handled automatically via what's called Auto Exposure. Many engines use systems that mimic camera controls for Auto Exposure, which makes the in-game camera behave like a real camera.
The problem between how it looks in a game and in a movie, is that in a game YOU are controlling the camera and so the game doesn't know when things will get bright or dark, so it has to make it automatic. In a movie, camera staff don't really use Auto Exposure and instead have someone in charge of fine tuning the exposure throughout filming, so you will get more appealing exposure changes that don't grab your attention (unless overexposed or underexposed visuals are the focus of that scene).
Ray Tracing will do nothing to fix it, and things like HDR have higher ranges so the exposure doesn't have to shift around as much, but it will still do it. The only time HDR will be able to get rid of Auto Exposure is when the panel is able to display as dark and as bright scenes as needed in a game, and by then your eyes will be the ones doing the work (and the panels will be as bright as the sun seen from earth, so good luck playing some games in the middle of the night — you will go blind :P). But really, Auto Exposure can be tuned a lot, and the algorithms are being improved constantly so things will get better.
The example in your video is a bit strange because it also goes darker than it should, it seems, so it could also be the game having volumes with different color grading settings on it and it just blending from one to the other. I would have to go to that same scene and look at it, because I don't remember how it reacted. Volumes with different colorgrading are also very common, but you can run into problems where you're looking at the same thing and suddenly the whole screen goes brighter or darker for "no reason" (other than your camera having moved from one volume to the next).