I have a Java project in IntelliJ to which I just added a bunch of files in a nested folder hierarchy. Many of these files are tests and include the main method, so I should be
The documentation you linked actually has the answer in the link associated with the "Java class located out of the source root." Configure your source and test roots and it should work.
https://www.jetbrains.com/idea/webhelp/configuring-content-roots.html
Since you stated that these are tests you should probably go with them marked as Test Source Root instead of Source Root.