Well, got around to trying Grand Master Chess in my win7 VM [Virtual Machine] as a work-a-round for those asking in the comments about a windowed mode -- no go -- someone else may have better luck but for me it just wouldn't run there. Did come up with a fix for anyone having trouble running the game in compatibility mode, &/or it works if you just don't want to wait for the video to play each time you start the game...
All I did was replace the intro.avi file with a new 1, 100ms in length, showing a black frame. The way I did it was create a 640 x 480 image [Windows Paint will work] filled with black & saved as a .bmp file. Next fired up VirtualDub [virtualdub.org], went to the Open video file dialog under the File menu, selected Image sequence for the file type, then selected my black .bmp file. Under the Video menu selected Compression, then selected Microsoft Video 1. Under the File menu Save as AVI.
Grand Master Chess still takes a moment or three to start, but I don't think quite as long, & during that time you just have a black screen.