The father is said to speak “as though the state of being alive were itself a sufficient cause for happiness” because the author of the article is affecting to regard the proposition that “the state of being alive is itself a sufficient cause for happiness” as obviously untrue. This is a standard irrealis use of the past form, which you have probably encountered in conditional constructions:
If happiness were itself a sufficient cause for happiness, then Jessica’s father would be justified in his statement.
The author wishes us to understand that (in his opinion) the state of being alive is not itself a sufficient cause for happiness. On the contrary, the state of being alive is (again, in the author’s opinion) “a prison of its own, at least in a phenomenological sense”.
I hope I need not say (but plagued as we are by the ineluctable anti-intellectualism and philosophical naïveté of the popular press and of so-called ‘democratic’ education, I feel I must) that this is intended (albeit meretriciously and by way of an inauthentic and false-conscious ressentiment) satirically.