I am an avid gamer, I use Windows & Linux, I would like to play games in my Ubuntu machine which requires DirectX.
How can I run the game which requires DirectX in Linux?
You can use Wine.
Here is the Wine Application Database where you can check how well an application/game works with wine.
Here is an introduction article on How to install DirectX in Linux
Then there is CrossOver a commercial product that I have used in the past with decent results.