For starters, your logs say you are using the public build, when you, as a subscriber, have access to the more recent private build. I recommend you download that instead.
The bottom of your logs before the error message show: Module not found : /Users/[your user name]
I'm not one of the devs and I don't know exactly what that means, but over on Discord another user had issues with Stencyl's installation/not showing up, and it appeared to be an issue of multiple windows accounts on the same computer and administrator privileges, or somethinfg to that effect. So perhaps that's something you could investigate.
Another thing you can do is open Stencyl, go to Tools > Workspace > View Workspace Folder for this Game, and copy that folder. That can act as a back up. You can also go to File > Export Game, and the generated .stencyl file is another )and preferred) form of back up.