So the question is how important is it to gaming?
The answer is: Not much. HDR doesn't improve gameplay, it doesn't doesn't give you a new way to play, it doesn't add new effects of dimensions to your games... It does give you better colors and contrast... but besides a couple oo-ah moments it doesn't add a whole lot to gaming.
The reason why Microsoft and Sony are pushing it, however, is less for games are more for other media (streaming predominantly).