One more thing:
The thing I think contributes the most to this game's impact is how beautifully synergistic everything is and complements each other.
Most games are quite accidental in their design, when they happen to be awesome, it's mostly through luck. Admittedly, making perfect or near perfect platformer is much easier task than making a perfect RPG, because of how constrained platformer is in comparison, but it's no small feat - here you have too big a pile-up of stuff to seriously consider product of luck - even small things like semi-interactive cutscenes featuring other, much less agile character (Naru) priming player for how the basic movement and physics are calibrated in game, or how music keeps playing if you get killed and respawn (I'm not the first to make this observation) keeping you in the action and spun-up, or how its pacing in tense sections like escape sequences matches general pace of player movement (timing of wall jumps or rapid bash sequences), effectively helping propel - forcefully if need be - the player (especially less skilled one) through the otherwise traumatizingly frustrating moments (I wasn't joking or exaggeratingabout some sequences in Horu when I said they got me laughing hysterically - it felt idiotically optimistic at the time that someone made such a sequence while thinking that people will be able to complete it - the fool - and I was really just sitting there emitting this hearty, yet joyless and overall hopeless laughter). Having the awesome soundtrack constantly hit you somewhere between soul and gonads really helps you grit your teeth and tell yourself that now you will be those few ms faster, more precise, more perfect and fucking beat this fucking thing.
Another interesting thing is that - in no small part thanks to the constrained nature of a platformer - Ori manages to nearly seamlessly merge gameplay and scripted content - even outright cutscenes tend to be at least semi interactive and retain consistent control scheme with the rest of the experience because the movements, even predetermined ones that you just trigger in full cutscene mode just feel like natural response to your input.
Speaking of input, while original keybinds are bad and control scheme could use some refinement for superior HIDs (KBM), kinaesthetically the game is just glorious - Ori's animations adapt smoothly to the environment and the mobility itself is just glorious, early in game you already get powerful stuff like wall and double jumping in addition to just Ori's natural speed agility, later you can rapidly (but by no means efortlessly, at least on your - player's - part) cross vast portions of levels without even touching scenery (and will need it too because spikes, lava, spikes in lava, and lava filled spikes, also lava) and it feels great, especially when you're soaking in the visuals, atmosphere and OST.
Lastly, Ori is an irresistible protagonist. You see, the character you play as, whether predefined or customized is important. If you can't like the character, or identify with them or some part of their goals, or find some other reason to accompany them, you will soon feel bored and detached at which point you will quit. Ori just happens to be the kind of critter you physically cannot dislike or not root for - cutesy comes packaged with extreme agility and grim determination. It's hard to not care for Ori, because at this point someone just has to. OTOH I probably wouldn't be able to play any, say, Rayman game, because Rayman's design - just the face alone - trigger irresistible punching reflex in me and this is unhealthy for my keyboard.
The character that generally relies on cunning and speed to avoid threats also feels quite refreshing and easier to root for (because there is just no drama when the nominal protagonist can just steamroll stuff) and (this is not just my own observation either) it's fitting for such character to be engaged in escape sequences in place of boss battles.
Finally (I lied when saying "lastly") good antagonists are sympathetic. While inexplicable assholes are by no means unrealistic, they add certain amount of futility to the story. Just like it's generally not good design to just randomly kill player and just like you can expect some sort of fairness from a game even if life generally isn't fair, antagonists that aren't just random assholes make for better stories. For such a simple game Ori weaves everyone's motives, knowledge and means quite tightly into the story, so it flows well while also featuring some treats for the observant player.
I am not a plaformer fan. I consider, perhaps wrongly, most platformers to just not be worth of my attention - but Ori, hitting me simultaneously from all directions with its concerted implosion of full spectrum awesomeness has proven to be impossible to ignore, it hooked me on the first contact and - if it's not readily apparent - it hit me HARD.