Dig Dug has a problem, he has to clear the monsters out of the ground by any means necessary. The means that he has available to him are: smashing them with boulders, and using his air pump to inflate them until they explode, sounds pretty gory.
Dig Dug can dig (and, by extension, dug) through the ground either up, down, left, or right and needs to make his way toward the pockets of monsters, and to carve out traps to make use of the strategically-placed boulders. The only weapon he has, other than his fantastic cunning and smart white jumpsuit, is an air pump. He can send out a line, lodge it into a monster, start pumping away, and the monster will inflate and burst.
The monsters start out pretty stupid, but they quickly remember that they have the ability to travel through the dirt, where there are no paths, straight to Dig Dug, who is likely going to be immobilized because he’s busy inflating something or other. Then he dies.
I may be being a tad harsh on the game, it’s actually fun for a few levels, before the ridiculous amounts of enemies surround you before you can form a plan. But that may be just me.