I answer myself, after a more thorough reading of the documentation.

The URL to get the rendered document is not in the /api/v1/etc… , but in the nxtemplate namespace; the URL nxtemplate/document-path@model-name renders the document and returns the rendered result.

Example: GET http://nuxeo.mycompany.com:8080/nuxeo/nxtemplate/default/stages-conventions/convention-test-eleve-01@stage-convention-modele-01 … returns a docx binary file, Where:

• stages-conventions is a workspace directory,
• stage-convention-modele-01 is the name of a nuxeo template containing a docx template document
• convention-test-eleve-01 is a nuxeo document associated with the template