Each player would draw a grid on a piece of paper and... well, you know how this works.
However, board game makers began to stick their noses into Battleship in the 1960s. In a large and colorful box, a new version was heavily marketed. All that was inside were three small pads of paper with printed grids on them and a huge game logo at the top. There were also two stubby pencils inside. And that was it. Now this was a popular gift to give to kids you didn't like much. There was also a deluxe version for kids you really hated, with each paper having a slick wax coating that would not take a mark from a pencil, pen or crayon.
Then came the era of battery-operated home games, so a new version of Battleship was made. Now you had flashing lights and the sounds of explosions. You also had tiny plastic peg markers to use and lose. This loss would only be a temporary thing as you just knew your little sibling or dog swallowed it.
Finally came video game versions, with animated ships and explosions. However, even an MMORPG version with pirates and loot boxes failed. This was discovered to be because none of them included blood and gore and the screams of drowning and burning sailors as players expected.
Today, Battleship is still played as the paper-and-pencil game, but only by the gnomes plotting your death and skunks living in your backyard.