What movie are those screenshots from? It looks vaguely familiar but I can't place it.
That said, I've had similar ideas for a game for a long time, I think as Yahtzee points out a lot of people have. Getting around the "murder simulator" thing would be simply to give the protagonist-killer a sympathetic motive of sorts, as far as such things go. Have the protagonist be cursed or something, and some eventual meta plot leading to them being freed from their curse at the conclusion of the game.
That said I had the thought largely in regards to open world crime games, especially Saint's Row where you could wear weird costumes and stuff. The missions largely being what Yahtzee describes, but the game also being designed so the various "rampages" don't have to be kept entirely separate from the main storyline.
One of the big reasons I thought of it as well is simply because there are computerized/organizational systems like the old VICAPS to predict criminal behavior and assist with the apprehension of criminals. I was thinking part of the missions could be playing against the equivalent of such things, with degrees of success coming not only from killing but doing it in such a way that makes you harder to catch. Leave behind too much evidence and there would be penalties where the police eventually raid your horror bad guy lair in the abandoned basement under the local high school, or on the 13th floor of an insane asylum or whatever. I envisioned the game as having a sort of "terror meter" or whatever which goes up from things like torture and messy kills, which of course makes things harder to get away with, and losing your lair and trophies would reset that making you comparatively weaker, some missions might also require a certain level of terror to be present.
