The point EJ Lowe is making is about "metaphysical realism" - not "realism". Metaphysics is a theory about first principles. Metaphysical realism would therefore be a theory about the first principles of reality. Therefore, metaphysical realism assumes that there is something fundamental we can say about reality. Whatever those first principles are, they claim to refer to the essence of reality.
What someone means by realism depends on their worldview. For example, Jo Wehler in his answer assumes materialism, so in that case realism is about physical objects. There is some degree of essentialism in materialism because it claims that reality is comprised of things with fundamental physical properties (i.e. essences). In the answer by Geoffrey Thomas there is no well developed metaphysics assumed, it could be events or objects or something we have not yet defined. But Geoffrey is making an assumption about mind, so there is a hint of essentialism there too. We don't have a clear definition of mind, but Geoffrey assumes that it can be independent of everything else, that seems to assume some first principle about mind (i.e. at least a partial metaphysics).
An idea that might be helpful is representationalism, for example, both Geoffrey and Jo seem to be assuming representationalism - that language can represent reality. So when we say "mind independent reality" that represents something that is independent of human language.
Representationalism assumes dualism which assumes essentialism (mind being an essential or fundamental property). So a realism that assumes representationalism could be linked to essentialism. That is at least what I tried to do in the example with Geoffrey.