Similar to what occurred with Fritz 13, I had to overcome some issues while installing the Chessmaster: Grandmaster Edition DVD onto my new Windows 7 laptop. The DVD autorun file didn't work at all, so I had to find the setup.exe file in the English-language installation folder on the DVD and create a shortcut to it on my desktop. I then edited the shortcut properties (via right-click menu) to have the program run in Windows XP compatibility mode and as an administrator. As a precaution, I also disabled the McAfee virus scan software for the duration of the installation.
After this, the installation went fine, although I discovered that you have to let the install program try and install DirectX, even if you already have it on your computer.
If anyone else has problems with their installation, this may be of help.