There is some non-linearity in the 2D games. In the first game, you can do some of the dungeons out of order. For example, some people like to save dungeon 6 for last because it’s difficult. Some dungeons do require items from previous dungeons, but not every one.

A Link to The Past also has some nonlinearity in the same way. The dungeons in the dark world are numbered, but you can still do some of them out of order for the same reason as the first game.