One factor that you're leaving out is the moral horror of painfully slaughtering these giant and beautiful creatures. Often the colossi are completely benign, and you have to figure out a way to injure them to get their attention or bring them down to your level. My wife watched me play the first level, and left the room horrified.
Thus, the emotional reaction of the player is a key component of the art. I began the game tackling the first colossus with feelings of guilt and shame for being such a butcher, but that was tempered by the knowledge that the kill was a necessary act. You have a love to save, after all.
However, as you progress through the game your revulsion subsides. You become numb to the screams of pain, the frenzied attempts to shrug you off. It becomes simple sport, instead of a vile but necessary act. The kills devolve to "just a game". Your character physically reflects this, as you become gradually darker and deformed, but at such a slow pace that you don't notice until the corruption is quite far along.
And then, at the end, after you thrill to the final hard-won kill, the morality comes rushing back. What you've done was wrong. Evil. Even though you set out with the best of intentions, your soul is now irredeemable. The guilt is intense. Then, finally, redemption of a sort.
SotC is emotionally richer than most films, and the responses that it evokes would not be possible in any other medium. SotC is art of the highest caliber.
The gameplay elements are integrated into the storytelling in a way I can only describe as art. Desolation, terror, desperation, and triumph experienced in the gaming elements are as well integrated into the story as the best soundtracks are integrated with the best made movies.
The experience of holding on by your fingertips, as the grip bar shrinks, the horror experienced when scoping out the 8th colossus from a distance and letting it close with you, the hopelessness of operating the last character to appear... these are all integrated with the emotional intent of the part of the story they are in, to the point where the gameplay is integral and not a bolted-on gimmick.
Interactivity is just another element, like color, sound, music, CG, 3D, or any number of technical innovations. It's just another tool to be used, artfully or clumsily. It may start out as a gimmick, but creative and talented people will figure out how to properly integrate it over time.
(Yes, soundtracks, color, CG, and 3D were once all pronounced to be gimmicks that added nothing to the art of movies.)