Uh, this is bad - really bad. It means that Java is not able to create native frames/windows on your machine.
I will try to reproduce the error, but since this happens right on startup we should have encountered this problem in our pre-release tests if this was an issue for our test machines as well. To be honest, even if I can reproduce the error, I am not sure it can be fixed on our side.
In the meantime, can you uninstall yEd and install the variant that comes with embedded Java 8 runtime environment? A corresponding macOS disk image is available from https://www.yworks.com/downloads#yEd.
That is very good news!
Such information is stored in the yEd profile directory.
A word of warning: Deleting the profile directory will also delete any user-defined palette sections and custom properties mapper configurations as well as reset any custom preferences to their factory defaults.