The example I've always use for how gameplay can make a scene more emotional is the end of your first battle in Shadow of the Colossus. You know your main character has been tasked to slay these massive creatures to bring back his dead love, but there's little information about them. It just lumbers slowly into view when you confront it, and what follows next is one of the most tense battles I've played in a videogame. You're clearly outmatched, a young man who barely knows how to swing a sword against this massive moving monolith, but you somehow manage to succeed. Just as you're ready to cheer out in victory as it falls, the game takes a shift. Instead of the triumphant battle theme, the music turns soft and sad, and you watch your foe slowly tumble down. Instead of glory, you feel regret, and your victory now seems like a tragedy.
Seeing that in film would be emotional, but it's not some character doing it on a screen. You did this, and you killed this strange and magnificent creature. Was it worth it? There's a similar example in the ending of Metal Gear Solid 3, but I'd rather not spoil the amazing ending of that game (which would generally works as well in film, except that one particular moment).
No, you have years of experience in a medium that prepared you to interpret that event a certain way.
"it was because you were prepped by playing the game to experience that scene in a particular way."
That's like saying, "Yeah, I jumped into the Iliad at the funeral games for Patroclus, and I just don't get it: it didn't have an impact at all." Duh. The literary experience leading up to that event leads to a connection to the characters that has little weight if you skip it. Saying the same thing applies to video games isn't an argument as to why video games can't be expressive. It means they can, and you have to invest in them to have that experience, much like reading a book.
And the best games aren't "built around" movie-like cutscenes. But suppose they were, and that those scenes were evocative. How, exactly, is that a bad thing? It's not, unless you've a priori decided it is.
Actually, my point was just the opposite. You can appreciate a passage from the Iliad or a scene from a movie without context. Not fully, but there's something there.
Since I've heard about Aeris being killed by Sepiroth before, I went ahead and watched it on YouTube, and I wasn't impressed. It must have been because I didn't play the game. If that scene affected you at all (if it looked like anything but cheesy crap animated with expressionless plastic dolls) it was because you were prepped by playing the game to experience that scene in a particular way. You can watch a clip of "La Strada" or "Midnight Cowboy" or "Unforgiven" or "Casablanca" out of context and at least get a sense of the emotional dynamics of the characters. That's the strength of movies. The strength of games is the immersion and feeling of personal involvement with the characters, personal involvement driven by your own actions, choices, and sacrifices. I may have felt like Ratso Rizzo was my friend, but I never picked up a john to get money for a bus ticket for us to leave town together. I may have shared Rick Blaine's feelings as he put Victor and Ilsa on the plane to Lisbon, but I didn't decide to do that. It just happened to me.
Games will always be second-rate next to movies when it comes to presenting scripted drama, but they don't have to feel that way. Aeris and Sepiroth is proof of that, I guess. Gameplay allows games to affect us in ways that movies can't and enables different and stronger emotional contexts for experiencing games as art. The art of games is in the gameplay. Detaching from gameplay is just a crutch, like filming a stage production, copying another art form because we don't understand the new one well enough yet.