Right click on the main executable for the installer and go to Properties. Click the Compatibility tab and trying selecting either Windows Vista or Windows XP. If that doesn't work, leave that setting as is, right click the installer executable again, and this time select Run As Administrator.
Hmm... after a bit of Googling, seems a couple of Myst's files need to be patched in order for the game to run under 7. Details can be found here.
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