What I make of it:
After his loved one (girlfriend? wife?) died (suicide? - maybe she jumped off a cliff?) he decides to save her by jumping off a cliff himself.
Then he gets to Hades (the "underworld") himself.
He fights Ceberus
(in Greek and Roman mythology, it's a multi-headed dog which guards the gates of Hades, to prevent those who have crossed the river Styx from ever escaping) and eventually reaches his loved one spirit.
He then try to escape Hades along with her, they reach to her grave only to find out they can not return.
I guess that's why the game is named 'Don't look back'.
Anyway, it felt like a dark, yet good, Atari 2600 game. Not bad at all.