Existential responsibility started long before Nietzsche and company espoused those virtues, dating as far back as Aeschylus in his portrayal of Prometheus, the giver of light:

I know exactly every thing/That is to be; no torment will come unforeseen/My appointed fate I must endure as best I can/Knowing the power of Necessity is irresistible/Under such suffering, speech and silence are alike/Beyond me. For bestowing gifts upon mankind/I am harnessed in this torturing clamp.

For I am he/Who hunted out the source of fire, and stole it, packed/In the pith of a dry fennel-stalk. And the fire has proved/For men a teacher in every art, their grand resource/That was the sin for which I now pay the full price/Bared to the winds of heaven, bound and crucified (ll 101-111, Aeschylus, Prometheus Bound)