If you go to your library you should be able to download it from there. Just click the arrow in the top right corner next to your name. But the download button at the top should lead you there as well.
I'll provide a step-by-step on how you can manually tell itch.io which games you want for it to update. I do it manually just to avoid being clustered :).
1. Open your itch app, and check the bottom left corner for a button called ''Downloads''.
2. Open Downloads and the first thing you should see is a list of the games that have been updated by their developers. ( Note: you can choose to update all of your games with the ''Update all'' button, but it's going to take a lot of time if you have a lot of games on the updating list)
3. For a individual update, you should select Mannequin Academy, or any game you wish to update, and click ''update now''.
4. A new window is going to open and you have to select and click the bellow circled option (I'm going to use another vn from my list as an example):
5. Wait for it to update, the speed of downloading really depends how large the update is and your internet, so you should wait for it to fully finish before launching the game. You can check if the download is viable if it shows up in the bottom left corner like this:
6. You're done! You can now continue playing the now updated game.
Hope this helps!