Microsoft DirectX is a collection of libraries for game programming. With Runtime installed on your Windows Desktop you can run the most important commercial games.
On linux you can’t have DirectX installed natively as part of system and there isn’t a Linux Binary versione of it. So, you can’t run windows games on Linux. To have DirectX games on your Linux you can try Wine. Wine (wine is not emulator) is a wrapper of windows libraries, so you can use windows software on your Linux Desktop.
Many of windows software don’t run on Linux with Wine, but you can try particular configuration of Wine to see if you can run your favorite windows game or software.
To install a Windows Game on Linux you have to install and configure DirectX on wine. This tutorial explain how to install DirectX.