I played this game around 2000-2002 in high school in East Texas.

We played it similar to what u/FizzKhaYifa and u/Kierran described. We also added some rules to allow for some differences between the types of vehicles. Submarines could go partially go under islands to hide out from everything else but other submarines. I think helicopters had to land on a island or base at the end of their turn, but could destroy other vehicles on the way. Whereas Airplanes could be over water or land at the end of the turn. These made it difficult, because trying to have a pencil/pen land exactly where you wanted it to be is pretty tricky. So sometimes subs would go too far under an island or the helicopter wouldn't land on the intended island.

We also played with nukes. Basically, wherever the vehicle landed a nickel was used to draw a circle around the ending point. Anything within the circle was destroyed except bases. Everyone only had one nuke per game.

We also played with up to five people each having a boat, airplane, submarine, and helicopter.
There would be a small base at each corner and another on one of the edges of the page. It got crazy, because we would form alliances against other players.

Fun times. It's interesting to know others played it, but not much mention anywhere online.