For your information, in the meanwhile you can install the app using itch.io's official desktop app. It's quite a bit of a hassle initially, but it has the benefits of enabling auto-update for Mannequin whenever the itch app is running. Mannequin itself has no DRM, so you can just launch it after installing without keeping the itch app running at all times.
Just to confirm, I was in the same situation and saw the same problem (macOS, downloaded from the website); installing via the itch.io desktop app fixed it. My guess is that it expects the library folder within the archive to be in a specific location.