Hi there,
The behavior of the Steam 'Stop' button is different depending on the platform (Windows, MacOS, or Linux). On Windows, Steam will send a WM_CLOSE message to the app's Windows. Elsewhere, a kill signal is sent to the game's process.
From your depot, it looks like your game is a Java-based game. It's possible that your game isn't properly handling the WM_CLOSE event. You may need to import the appropriate Windows DLL to interact with the Windows message pump and properly handle that message.
I would recommend posting your question on the Steamworks Development community forum. It is very likely that a developer there has encountered (and potentially resolved) the same issue that you have.
Best,
Steam Support Team