You can put an icon on your desktop. It doesn't really address your request as it just loads the app against the website like the other solutions, but it's a little better.
Assuming you've installed the app in Chrome (there's both an app and an extension), go to the apps panel with the
chrome://apps/ url. You should be able to find a big tile with the stackedit icon. You can right-click this icon and there's an option to "create shortcuts". Under that there are two options: one will put an icon on the desktop, the other will "pin to taskbar".
According to the app page in the Chrome store,
Documents are stored in the browser's local storage, which means they are not shared between different browsers/computers. Furthermore, clearing your browser's data may delete all your local documents.
I think that means it works offline, and you'd have to "publish" it to somewhere to store it.