The information about this game says that it has nonlinear exploration gameplay, but does that mean that the story itself is nonlinear, or does it just mean that you can explore in a nonlinear way, but then the story is completely linear? Are there any choices to make that would alter the story or the dialog in any way? I just want to know this, because it's a deal-breaker for me, as for whether or not I would play the game.

It's the latter. Some puzzles can be completed in a non-linear order, but the story itself isn't affected in the slightest.
There are no choices throughout the game - only at the very, very end you can make one decision between two, to trigger the credits.
Note that sadly your save gets deleted afterwards, so for the other ending you either have to replay the whole game or visit good old friend Youtube.

Or just make a copy of the save file before finishing.

EDIT: But even so, a game deleting its own save files without permission is an atrocity, and should be considered a very severe crime!