So far, the plot is a little thin in this game, it seems to consist of people impeding your progress to make you solve a puzzle, but the puzzles have all been really great so far.
For instance, so far into the game I've come across one of those "take animals across a river with a raft but you can't have more of one kind than another on a side" puzzle and the "find which weight is the lightest out of 8 using a scale only twice" puzzle.
So if you like logical and lateral thinking puzzles, and you also like beautiful Miyazaki-esque visuals, this will pretty much be game of the year for you, I'd say.
Watching that trailer, I can see how it would be considered non-canonical. If the cliched amnesiac's actions were so important, then he would have been protrayed in show. So really its just 'pretend your a character on LOST.