The originality stays in the fact that you don't interact with things in the usual way (not that much, at least) but have to... think your way out of the situation. Literally.
You wander a lot, but just through memory, covering a lot of physical space and, of course, time itself. This looks like an answer to the challenge Andrew Plotkin put on IFMud some time ago: you had to make a PG where time and space were stretched far beyond the limits of the medium.
As stated by the author, Enigma is a sort of experiment. To what extent it's a winning one, you have to play to discover.
Subjectivity plays a major role, here, in my opinion.
The game is a sequence of images which follow one another, triggered by a single action. The object of said action changes according to the latest bit of text you've read. By actually >THINKing about something, the PC pulls out a bit of memory in which is "hidden" the next thing to be thought over. Sometimes you can look (around and at objects) to see if something has changed and to get a new piece of story. To me, the consecutio was fun and satisfying, until I got stuck and resorted to the walkthrough. While the mystery unfolded, I wanted to keep playing -- just for the sake of knowing more, and the pacing was quite perfect. This sorta trick may not fall in everybody's tastes.
The central meta-puzzle (understanding you have to >THINK, rather than >DOWHATEVER) could have been better hinted at: although you find the solution in the very first sentence of the blurb, it escapes you until you are pointed at it. Such a mechanic is worth showing, not hiding between the folds of a pun. Anyway, you eventually end up doing the right thing, so maybe I'm overreacting.
Speaking about mechanics, there's a lot to be said about Enigma.
The first thing that struck me was that, maybe, this could have worked as a WB as well, if not better. Once the trick is understood, what you do is actually typing the next noun, where the verb stays intact. This could be achieved with far less struggle in a Twine environment with no doubt. (This said, the author confesses in his ABOUT text that Enigma is "not representative for the medium", so I shouldn't argue. And experimentation, to some degree, should always be welcome.) My second nosy accusation could be that, in the end, there is too much "guess the verb", although in the given case I would call it "guess the noun". Trying to avoid reading every single sentence out of context to find the right object or memory to think about, I had a hard time, later in the game, in finding what to do next. Fortunately enough, a MODE command can be used to highlight every useful topic in the text, although this partly spoiled my experience. (Did I ever say I hate walkthroughs? In the same way an alcoholic hates the bottle: you just can't keep your hands off of it, but you know it will ruin your life forever).
The engine of Enigma looks very well polished (I counted just a couple of typos, and being non-native speaker I may very well be wrong!): much of the text subtly changes after we've seen and thought about things, or after something has occurred. Given the sheer number of cross-interactions, I bet this was a nightmare to code. The text itself is, by means of playability and fairness, reduced to the bone: this doesn't play in favor of a very brilliant prose, but actually helps the player stay focused.
On the other hand, though, some things work in a confusing way if they don't occur in the right sequence. What comes to mind is when you have to think about three steps of a trip, for the first time: when you are at it, something important has yet to be discovered (at least in my play-through) and then you have to think about them again, to advance the game-state. That could be nice if it was not for the fact that almost no other "thought" gave me different answers when tried twice (if not for the aforementioned syntactic reasons). So, be warned: you are actually encouraged to repeat thoughts.
One last thing that struck me as unfair is the Undo Prevention at the end of the game. I understand this is intended by the author, but can't fathom why. If it is for the sake of replayability, sorry but it doesn't work: the only branching moment I could see (and this is where I can be totally wrong) is in the very last command. I sense -- well, ok, I know due to having read the walkthrough -- that there are more than one ending. Why do you want me to repeat everything if 99% of the game is on a single track?
Let's wait until after the IFComp is over to ask for clarifications.
Story-wise, Enigma does what it promises to do. It's a mystery, told by the means of a clever trick. Reminiscent of Christopher Nolan's Memento, the story is quasi-told backwards. Stuck "in a blink of an eye", you have to realize what has happened, before deciding how to actually end the game (and probably your life). This is rendered atmospherically, and I loved the idea itself. To my slight disappointment, though, the mystery is not that much of an innovation and you will find yourself drawing conclusions (which will prove right) way before the first half of the story is over.
The expectations on the ending keep lowering as you understand that all is going right in the way you foresaw: the PC is traumatized by something, involving someone, and whom he's looking at is but in part what he thinks he is. Adding to this, the prose is full of nice double senses that, due to said expectation, all become more of a "one sense". Like overhearing a porn-movie where people hint at cucumbers or the likes: you would hardly think about vegetables, wouldn't you?
Overall, I liked Enigma a lot. The idea was original, at least until the plot kicked in, and the mechanics were working and sleek. To my poor disadvantage - again!- the walkthrough spoiled the fun (they should really ban them to cloud nine...), but I still can see a nice game when I see it, spoilers or non spoilers. I suggest you forget about the hints and time constraints of the Comp (you don't need that much to finish the game, anyway) and dive deep into it. The story... well, it's exactly where you would expect it to be. Still, you don't really need a perfectly new story, as far as it is well told. Right?