Contra (NES)

How I would sum this game up:  The video game version of what you played in your backyard with fake guns.

So you see the two dudes that you play as on the start screen.  They were modeled after Stallone and Schwarzenegger, who at the time were just reaching their pinnacle of action movies.  If you were a kid at the time, you probably idolized them and played was as them in the backyard.  Maybe you still do, who knows.  That is the reason this game works.  You don't need to know why you're fighting, or why there are turrets sticking out of the mountain.  You don't even need to know why the giant alien lives atop the waterfall.  You've already imagined this game dozens of times in your backyard, you already have created the back story for it.

Inevitably, in either scenario, a girl would say she wanted to play and you'd have to explain to her that she wouldn't know how to play.