You can publish SAS Report output (srx) from EG to Web Report Studio using the Publish menu. If your SAS Report output was created using one or more stored processes, the results in Web Report Studio will be "refreshable", meaning that you can refresh the report and it will rerun the stored processes for the latest results.
When you publish a report, you have two choices: publish to a channel or to the report repository. The error you cite indicates that you published to a channel. To share a report with Web Report Studio, you need to publish to the report repository -- an option that is available only if you have configured the report repository web service with Web Report Studio.