I came to this conclusion after playing STALKER 2, which makes particularly good use of HDR (albeit exaggerated by using auto exposure too). Beyond the purely aesthetic effect of making things brighter and more colourful, it can actually have an effect on gameplay.
- Assuming a bright enough monitor, it makes lighting part of tactical decisions, for instance it becomes a disadvantage to attack someone while facing into the sun, or to look at a bright light while creeping through the dark.
- Increased bit depth makes it easier to see in the dark by adding more shades of grey instead of everything dark becoming black.