more underexposure according to that image
Doesn't really have anything to do with exposure. You can have a perfectly exposed image and then apply too aggressive of a contrast/gamma curve resulting in crushed shadows and blown out highlights.
Black crush is essentially where all the darker parts of an image, instead of
only the darkest part, are "crushed" to black. Along the same lines, the brighter parts of an image, instead of only the brightest, are pushed to complete white.
This means any detail in those shadowed or bright areas simply vanishes as it is showing one single black/white color.
I don't know if this will help, but here's some examples from video editing that I'm working on right now. This is what a contrast curve looks like. The lower left is complete black, and the upper right is complete white.:
Now here is the RGB parade, showing the levels of red/green/blue, matched with that curve. 100 is pure white, 0 is pure black. You'll notice barely any of the image is touching 100 or 0. There is still detail in the brightest and darkest parts of the image.
Here is the frame matching this curve and RGB parade. We see detail in the dark parts of his suit and the white parts of his shirt.
Now here is what an extreme curve with crushed blacks and overblown whites might look like. You'll see the curve is clipping the black and white parts, essentially pushing the darker parts to complete black, and the brighter parts to complete white:
The RGB parade demonstrates this. Whereas before barely anything was touching 0 or 100, now we can see a solid chunk all along 0, and more pushing to 100. It's smushed the darkest all the way to black, and the brightest closer to 100. All that detail and visual information we had in the lower 3rd of the parade before the aggressive contrast curve was applied is simply gone. It's not there. It's all pushed into black.
Here's the frame matching the crushed curve and RGB parade. His dark suit is now just one black color blending with the dark background, and his white shirt is now almost one solid white color:
This is why crushed blacks/whites are bad. It may look more "colorful," his face is certainly more red/orange, the background is a stronger blue, but it's simply
eliminating visual detail that should be there in the brighter and darker parts of the image. Whether it's because of the game itself, the system, or improper RGB settings on the user level, you should want to avoid crushed black/whites as it is simply ruining the image. If you want a higher contrast or saturation, most TVs have settings that will let you play with those that shouldn't ruin the image in the way an improper contrast/gamma curve will.