Pre-print servers: Right retention applies to the author accepted manuscript rather than to the preprint version of an article (the version of your article prior to peer review). If adding the preprint version of your article to a repository or preprint server, you should first check the publisher’s article sharing policy. Many will permit this version to be shared.
Other repositories: With rights retention, the author grants their University a non-exclusive licence to make the AAM of their scholarly articles publicly available under the terms of an appropriate Creative Commons licence. This prior licence, and the inclusion of the rights retention statement with the submission, would allow you to deposit the AAM in other repositories under the terms of the same licence.
