I'm using Windows 8.1, but I assume this problem would be present in 7 (and 8.0) as well.
When you attempt to install as a Standard User (without admin rights) you are asked to get and Administrator to put in their password to allow the installation to progress. When you do that, however, the application is installed pointing at the Admin's user directories, which makes it impossible for the intended user to use as the stencyworks directory is owned by someone else.
For example, if "Joe" (a Standard user) tries the install, but has to get "MyAdmin" to enter their password to complete the install, when "Joe" runs Stencyl and clicks on the View Games Folder button, he is told that he cannot access the directory, which is in /Users/MyAdmin/...
In order to get around this I had to make the user an Administrator, get them to complete the install, then make them a Standard user again. After that all seems to function correctly.
This would suggest that the wrong user is being used in the install scripts when the user directories are created, which I would expect isn't too hard to fix. Alternatively, it might be possible to create the user directories before getting to the part of the install which requires admin permissions (placing the application in the Program Files directory).