Had the same issue. After you install the game thru itch's "install" button, - you need to manually launch the .exe without the itch inteface: just double click "Tentacles Thrive Alpha v4_07.exe" file in wherever folder it installed itself. Solved the issue for me.
The save file is called "TTv4_Save.sol" which should be in C:\Users\-user-\AppData\Roaming\Macromedia\Flash Player\#SharedObjects\-random text-\localhost\-your itch.io install path-\Tentacles Thrive Alpha v4_07.exe\
You can check if its being created/updated when you save your game.