I installed the Big Fish Games Manager (BFGM) via the C4P file, then I ran the Drawn installer stub.exe in the same bottle but as a regular app.
The BFGM opened, asked me for my credentials, and proceeded to download and install the game.
If you "install" the installer stub, CXG will not detect when BFGM finishes the installation, and you'll have to terminate the CXG installer by hand.
I've played the game for a few hours and it's very playable. Even when it inexplicably lost the audio, or occasionally crashed, I was able to just rerun it and continue, because it autosaves very frequently. I never lost any progress.