RightousMan: @Spinorial I suppose this is possible but I've left it running for hours and it just doesn't finish.
That would be consistent, since the main installer would be waiting on the secondary directX one, without realising that something's wrong. I suggest you contact GOG support (unfortunately, they're a bit slow during the sales). They should be able to help you find some log files that might help them solve this.
HOWEVER, in the meantime, you can try the following: Start the installation and let it reach the point at which it stops doing anything. Leave the installer running and browse to the folder where you instructed the game to be installed. If my theory is correct, all the game files may already be extracted. So, copy the entire folder to another place, then cancel the installation. Now, try running the game from the files you copied. From my own experiments, KotOR is portable, so if all the files are there, it should run without issue (or at least up to whatever issues it might have with your specific system :P)