There are plenty of people who would argue that getting to end credits means beating the game.
You can however say that skipping levels also skips the story, so they did not finish the story.
OP didn't say they "beat" the game. If you want to argue that, it's a different discussion.
Ecco the Dolphin (video game) > Plot: https://en.wikipedia.org/wiki/Ecco_the_Dolphin_(video_game)