To be fair, I haven't watched the trailer, but the rest of the comments have outlined it for me.
But is sounds like it probably won't work. Depression Quest somehow managed, though I think that was largely a result of how the game was made; Text, and you were given choices. For each choice, something would still go wrong, and despite making all the 'right' or what seemed logical choices, your character would still end up feeling upset. That sense of no matter what you do, its not going to help, and having to take the long path through things to start getting better, is probably why it managed to whilst not have someone experience depression, at least give them some ability to empathise with those who have.
Rape, however, isn't something that simple. You could probably do it better with a text based thing than it sounds like this game is going to do, but honestly if you're going to do rape, I think you need to do the real deal of it. Not as in IRL. Have a normal game. Naturally, it needs to be known for its mature story. Don't advertise it based on rape at all. Have it seem to play 'normally' for whatever type of game you make it. And then have it happen. Preferably have it as a family member or friend the player has gotten close to, and make it confusing and in first person enough that they can't see what's going on, but eventually they can figure it out.
The game would also preferably be pseudo open world, and not have restricting goals and story such that you can say "At this point you get raped". More just you have a need to go to wherever it is you get raped in normal gameplay, and one time that you do it it happens.
I don't know if you could make a good game to tackle the subject, but that's where I'd start from. You can't just say "You were raped, run from the bad guy" and expect people to understand. That just sounds like a really poor taste setup for a horror game. Music is powerful, and a good soundtrack can help express feelings - but putting that into a basically horror/walking simulator isn't a great extension on that. You're better off just using the music by itself. You need to make at least that point of the game about rape, but not make rape a game.
Is it something that needs to be done? I don't really think so, but if people think it does then, well, whatever. Trying to spread empathy isn't something I can condemn. Is the way to do it? I don't think so.