HtmlHelperExtensions.DxaEntityMarkup method is documented as: "Generates semantic markup (HTML/RDFa attributes) for the current Entity Model."
Indeed, its main purpose is to render semantic markup, but as you noticed, it is also used for XPM markup. Note that XPM markup is currently not in the form of HTML attributes, but an HTML comment within the container element. As you see, it is initially rendered as an attribute which is later transformed into an HTML comment.
Note that "semantic markup" is broader than "Schema.org". In general, it outputs the semantics of the View Model (in RDFa format). You see a separation of concerns here: the View Model may have (public) semantics, the View itself doesn't know about those, but only knows where semantic attributes (if any) should be output. Similarly, the XPM markup may or may not be output (depending on whether the target is XPM-enabled), but the View doesn't contain that conditional logic.
So: yes, you should put
@Html.DxaEntityMarkup() on your HTML element representing an Entity, regardless whether your View Model has public semantics; it acts as a placeholder for semantic markup and XPM markup.
UPDATE (answer to Jan's question)
Note that Schema.org only defines a standardized Vocabulary/Ontology (types, properties and relationships), not a specific way to refer to those types/properties. Quote from the Schema.org home page: "Schema.org vocabulary can be used with many different encodings, including RDFa, Microdata and JSON-LD".
RDFa, in contrast, does not define a vocabulary, but does define how to refer to semantic types/properties using XML/HTML attributes. It was originally intended for use in XML (e.g. XHTML 2), but has been adopted in HTML 5 too.
DXA outputs RDFa compliant semantic markup. This can use the Schema.org vocabulary (see View Models from Core Module), but can also use any other vocabulary; it depends on the semantic annotations on your View Models.