Don't worry if a game installs another version of DirectX. The different DirectX versions don't affect each other.
If you had DirectX 11 installed, and a game installs DirectX 9, you don't get downgraded. You simply have another set of libraries installed. The programs that need DirectX 9 will use those libraries and the games that need DirectX 11 will use those ones. Same with DirectX 10.
Nothing gets upgraded or downgraded when you install another version of DirectX. They are all very separate.
It's like having Chrome installed as well as FireFox and Internet Explorer. None of them affects the others.
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The developers have to use a particular version of Direct X, depending on how they programmed the game. I program video games in DirectX 9 quite a lot, simply because I have lots of code produced already and it takes a long time to convert it all. And all versions of Windows since Win 2K can run it. (Wind 2K and XP can't run DirectX 11, so I don't write games using that version of DirectX).
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By the way, if you look at your uploaded screenshots, you'll see that in them you are running different versions of DXDIAG. That's why they are giving you different results. Blame Microsoft, though, not the developers of the games.