Amazing right? Even though it looks like it is L.A. Noire in the afterlife, I am worlds more excited for Murdered.
So back to what wasn't really touched on in the trailer. The guy you watched get murdered is Ronan O'Connor who got mixed up in the worst burglary ever and as the trailer states; he has to solve his own murder. How he does this is by using his newly acquired "ghost powers" to find hidden clues, possess people to get information or prompt other people with hints, and also aid other ghosts in Salem to hopefully garner their help.
I know what you have to be thinking, "Oh great, forced side missions." Apparently you would be wrong there. All of these other ghosts, or families of other victims, are completely side quests to fill out the world lore and not required to gain a thing or move on. Well at least nothing that will be required to progress.
Expect more information and game play sometime next week after Murdered is shown in more glory at E3.