"Cannot start compilation: the output path is not specified for module..."
You just have to go to your Module settings > Project and specify a "Project compiler output" and make your modules inherit from project. (For that go to Modules > Paths > Inherit project.
This did the trick for me.
You have to define a path in the "Project compiler output" field in
File>Project Structure...>Project>Project compiler output
This path will be used to store all project compilation results.
I'm answering this so that I can find the solution when I have to google this error again.
Set project compile output path to path_of_the_project_folder/out. That's what is working today.The intellj documentation makes it seem like we can select any folder but that's not the case.