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Okay, got it to work. For anybody wondering, right-click CTHCC in your list of games and select Version (bottom of list) and click on Full. This will install the game.
When you start it up, there probably won't be any sound. Press F1 to open the Properties menu and check the boxes for "Play BGM and ME" and "Play BGS and SE" to enable music and sound effects.
Trying to install this gives me Installation Error: There are no releases available for you to play. What gives? How do I install/play the game?