Spock's death is the climax of the movie, and we learn of and see his deep friendship with Kirk from the outset of the movie. Peter Preston was a nobody who lived and died soley to emphasize how ruthless Khan was. Likewise, we see Spock and Kirk interacting throughout Into Darkness. They bicker (as many friends do), but they like each other, although Spock doesn't quite realize what he has until he loses it. Kirk and Spock's prior adventures together in TOS do add to the WoK death scene, in the same way that knowledge of Wrath of Khan (and the entirety of Trek) adds layers to Into Darkness (i.e. the death scene being a twisted alternate universe version of the same event) but they're not "required reading", so to speak. They bicker like an old married couple. And as I said above, Spock doesn't realize what a friend he has in Kirk until he loses him. When Kirk is dying, he realizes what Kirk felt when Spock, his friend was about to die on Nibiru. But unlike Kirk earlier, he's utterly helpless to do anything about it.