I don't think that one can understand existentialism without understnding the historical matrix from which it emerged - which is late Christianity in Northern Europe.
Kierkegaard is well known as both as a point of origin of this line of thought and for his struggles with the faith of his ancestors.
Existentialism should also be understood as having deeper roots: the ancient argument as to whether essence preceded existence. Christianity, with its Theology of God and the soul assented to this.
It was the achievement of Existentialism to deny the transcendent altogether: The essence of man being the soul, the essence of God being not bound up with Being, that is existence. This was after Nietzsches Deicide - Kant had only hidden it behind the Veil of phenomena. Whereas materialism is strictly speaking only about the ontology of the physical world, Existentialism tried to provide it with a theology that centred on man himself, governed by himself wholly and consciously and posited a whole new set of values, as advocated by Nietzsche under the term authenticity.
Given all this, I'd align it with Ungers 'The Stuggle with the World', which reminds me of Heideggers being 'Thrown into the World'. It is also one of the meanings of Jihad literally 'struggle', and it is also the latter half of Gandhis Satyagraha - literally 'struggle to truth'. One is reminded here of the influence of Tolstoy on Gandhi.
I wouldn't class Unger as an Existentialist going by his early work Poetry & Vision (a brilliant essay), which he says informs much of his later work, and also by the Tanner Lectures, The Future of Religion; I would contend that Unger would point that Existentialism leads towards Nihilism - a destination that he rightly is wary of; and it is a charge that Sartre defended his philosophy vigorously from in Existentialism is a Humanism; it is also a charge that the contemporary French Philosopher Badiou appears to assent to, given now the benefit of history.