If you aren't scaling up text and UI elements based on the DPI then it doesn't really sound like your application is truly DPI aware to me. I don't see why that applies any differently to games versus any other kind of application.
If you want to see why, try mocking up a typical shooter HUD. Now try scaling up/down all the elements by 50% and see what happens. Feel free to play with the anchoring, etc. Chances are you're not gonna like what you see! Things get even more complicated when you consider that players with controllers often change their view distance when gaming and don't wanna reconfigure their display all the time.
The typical solution is to fix the UI scale to the window size, and keep the text large enough that it's readable at a large range of DPIs and viewing distances. If you can't get 100% there that way you'll typically add an in-game UI scale option. (The key difference between that and the built in UI scaling in Windows being that it's specific to the game, so you'll set it to something milder than you'd set the Windows option, and it will only affect the game so you don't have to keep changing it back and forth.)
[EDIT] I think I came up with a way to explain this that saves you the trouble of drawing it out yourself. The fundamental issue, view distance changes aside, is that games are balancing a third variable most apps don't have to: how much of the background--the actual game--is the UI occluding?
It is non-ideal for something like a traditional UI element where users may want to alter scaling settings to have more screen space if their monitor is close enough to their eyes, but for a game HUD that usually isn’t the desired effect anyway.
I think Microsoft made it this hard to enable the DPI-aware setting exactly because it forces developers to think about things like DPI. If everyone follows this guide and ignores it, then I predict that in a few years this setting will be ignored as well and a new DPI-awareness API will be released.