In interviews, Craig has insisted that Bond in fact is not out for revenge--hence "I never left"--but that M and others believe he is throughout much of the film. IMO, a weakness of the script is that this point is never clearly communicated. You can infer that Bond found his solace in the end by confirming that Vesper really was victimized by Quantum, and that getting at Greene was his means to that end. But since you don't know that that's what he's after until the end--and even then, as I said, you basically have to think it out rather than experiencing it with Bond--I don't think it's unreasonable for some viewers to conclude that it is a revenge film.
Not wanting to yank your chain, in spite of whatever Craig says or might say, how come his character arc is not about revenge in QoS?
Plot-wise, that's true, the plot is not about revenge, it's about discovering that there is a group called Quantum, who is part of it and what do they want. And then we see one of the masterplans unfolding.
But Bond's character arc is all about revenge in QoS.
Bond's character arc in Casino Royale was complete in terms of him becoming a 00, how he became one, how he used his status (a bit too gung ho at the beginning, where he actually does the unthinkable and breaks into an embassy), the fact that he needs to be a bit more cold-blooded not only in his killings, but any other actions of his as well.
In Quantum he deals with the consequences of what happened in the third act of CR.
He goes outside of what already is a shady system, and goes about his mission a bit like a bull in a china shop, because his rage is still there boiling just beneath the surface. And that comes for his betrayal.
He might not be sure if he wants revenge for Vesper's death itself or for her betrayal ("did she ever love him?").
The way he disposes of Greene might not be as cinematic in terms of climax as many might expect, but his act of leaving him in the desert is actually more sadistic than just shooting him in the head. He neither executed him nor did he bring him in for further interrogation.
Thus plot-wise, the plot is not about revenge, but about the villain's caper.
But his character arc couldn't be more about revenge. And of course that who/what caused Vesper's death is not a single villain but an entire group, which is a bit more abstract and wouldn't make much sense in the movie for Bond to seek revenge on an entire group that operates in such way on a global scale.
But it is Bond who drives the plot. And that is why don't understand why it wouldn't be considered a revenge movie.
Revenge, like betrayals and others as such, comes in many different shapes and forms. And for Vesper's death, he already had his, since he gave Quantum one heck of a blow and resolved within himselfthat particular issue of her death/betrayal ("forgive her, forgive yourself").
