You could imagine the curved parentheses as "cutting the corner" of the square brackets - or imagine the curve as just gently kissing the endpoint at a single point, while the flat square solidly includes it. "Open" makes sense because it satisfies the criterion that for any number in the interval, you can find a larger (or smaller) number that is also in it - there's "no end".
Visually, it looks like ) has more "room" than ], if that makes sense, and that "closed" would mean that the element defines the 'lid' of the range, while "open" means it defines the final extent.
But you can't argue with nomenclature, and extending the definition to the reals helped make it click for me, so I'm unlikely to screw it up again. Thanks!