For my Equella level of expertise (it's the first time I test it) and for the purpose of only quick testing, the Moodledocs is not clear enough. We should avoid to redirect to an external document for setting up the equella repository. Instead write all step instructions to setup up the repository in this document: http://docs.moodle.org/25/en/EQUELLA_repository
PS: from my test I tried first oauth2 but I didn't have anywhere to add the oauth2 id/secret into the repository instance. Then I tried the admin.jnpl, setup my shared/secret id, it allowed me to see the full equella site in the filepicker. I was logged in. I was expecting to not see the equalla site but a list of file that I could select. Either I'm doing something wrong, either something is broken.