Merleau-Ponty is a phenomenologist so his received view is "essence" in a Husserlian sense, as the ideal core of an intentional object, see What does Husserl mean by essences? However, he is also an existentialist, so Husserl's essentialism is revised along the lines of "existence precedes essence", see Bauer's Phenomenology of the Essence and Appearance in Merleau Ponty.
"The classical essence as Husserl’s description as being constituted by the mind in noetic noematic frame is replaced by contemplative awareness and non conceptual thought... Essence can be the very presence of the thing appearing. There can be the representation of the thing and there can be the appearing of thing. Representation is only one form of knowing. Representation is not experiencing the essence of what is."
So in the OP quoted passage the essence of time is seen as its direct presence to self, non-interpretive self-awareness, the "archetype of the relationship of self to self". In this view Merleau-Ponty is indebted to Bergson's analysis of time as qualitative duration opposed to the mechanical time of physics, which he saw as contaminated by spatial notions. In this regard Bergson's conception is quite close to Husserl's "time-consciousness", see Husserl and Bergson on Time and Consciousness. However, Husserl interpreted such self-aware presence as a "noetic" (experiential) component of the intentional act rather than as a part of its "noema" (purified object, essence), unlike Merleau-Ponty.