From the back of the box:
Things look hopeless!
Dateline - America: The nation is in turmoil. Cities are being crushed. Historic landmarks are getting pulverised. The armed forces are fighting back as 8 giant monsters ravage America.
Game play
The object of Monsters Ravage America is to become King of the Giant Monsters. Each player controls one giant monster and one branch of the armed services. As a monster, you want to destroy cities in America. The more cities you crush, the mightier you become. As a military commander, you want to protect cities from other player's monsters, or better yet, capture a monster and send it to Hollywood where it will star in B movies until it breaks free. After 20 cities are demolished the "monster challenge" is made.

The Ultimate Battle of the Titans
As every fan of monster movies knows, there can only be one star of the show. As America crumbles under the footsteps of these awesome creatures, the bravest monster will roar out a challenge to his foes. In the "monster challenge," an epic battle is fought. One monster will prove, if only until the next game, who is King of the Giant Monsters.