Quote: "do i need the redistributable on my machine or on the machine i want to run the game on it?"
On the machine where you want to run the game. (On your machine, on which the game was developed, the runtime environment was installed with the SDK. It is the other computer that misses the runtime environment.)
Quote: "The appropriate DLL is part of the redistributable package. That means you can make it part of the install of any application requiring it."
Yes, but there is a text file in the DirectX SDK documentation directory called "directx redist.txt", which lists a few files/packages which must be included in a DirectX redistribution. So strictly speaking, it is against the license agreement to distribute only one dll. For a quick test, just to see if the application can be started on the other computer, it works if you copy the dll into the same directory as the executable (unless you also need the Visual Studio redistributable mentioned above), but this shouldn't be an "official" installation procedure.
Remark: I recently installed a big, recently issued commercial game on my computer. While I watched the installation messages, it said "installing Visual Studio 2005 redistributable files" and "installing DirectX June 2007 files"... These are even older versions than what Dark GDK needs. I thought it will be interesting to mention that commercial games also need such redistributables.