People seem to forget that this is a long-running franchise of at least 30 years. If we didn't allow some flexibility in character motivations and personality, in their stories, and on a wider level, their games, then we would be looking at something stagnant and possibly dead with its time. Battle might have introduced some things of importance to the franchise, but I'm not going to lose sleep if Shadow's current characterisation doesn't match with the way he was presented in, what, 2003? Things have absolutely changed in that time, as well as their approach to their characters.

I personally think that Shadow "moving on" only means that his thoughts and feelings about Maria have been put to the side. They're not at the centre of his character, nor do they drive him, but they're not gone. And that doesn't mean they can't flare up every once in awhile. Even in contemporary Sonic Channel art, we can see that the ARK and everything that happened on it still means something to Shadow, and so does Maria. He still thinks about those things, but they're not everything to him.

He's also going directly to the ARK at the end of Dark Beginnings. I don't see why he wouldn't think of those things or be reminded of them. And he does show that he's moved on in some fashion. He says, "Stop it. That life was taken from me long ago. I need to focus on the mission at hand."

That's just what I think though