In general (I'm sure there are many exceptions), would you say 1-2 Player games are Solo games with the Co-op just tacked on? "This game is mainly Solo, but if ya wanna have a friend work together with you to beat the game, we'll call it a Co-op." As an example, the Oniverse games come to mind.
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Well, not all 1-2 player games are coop. Fields of Arle comes to mind. But they may be the exception, yes.