I've bought two games through itch, and using the desktop application it only downloads and installs the demo version of each game. I have to go through the website to download the full game.

I updated to v18.12 and one game is installing correctly while the other Va11-Hall-A is still installing the demo/prologue of the game.

Thanks for reporting back, I've opened an issue here and will try to see what's up: https://github.com/itchio/itch/issues/774