I'm a bit torn on the whole situation, to be honest.
First things first, this is a terrible interview - it's horrific timing and its massively disrespectful to the club and his teammates. Others may point to the fact that he says things along the lines of "nothing has been decided" and that the discussions will resume in the summer but make no mistake about the intent behind this interview. It will be an awkward dressing room on Saturday.
On to the bigger picture. IF (and I find it a massive fucking stretch) this isn't solely about money and it's only about ambition, then I can to an extent see the logic. Taking off the red-tinted glasses and looking at the situation a bit more objectively, to the rest of the world and to players LFC of recent years is a club that tends to sell their best players (maybe forcing them to stay one year longer than they want to), attempt to replace them with younger, cheaper players with potential. I know the Arsenal shouts have been met with derision by most, but footballers will look at Arsenal buying in players the calibre of Ozil and Sanchez compared to our transfer policy which seems to be exclusively based on potential that may never be realised or overpriced PL players, and you can see a discrepancy. We can argue the toss about what "ambition" really means when footballers say it, but usually they are talking about the players a club brings in and that they will get to play with.
That said, Sterling is 20 years old and in the grand scheme of things has achieved fuck all. To date he doesn't even have a full season of top class performances under his belt. He's had patches of incredible form (notably last season where he benefited massively from the space and time afforded to him from defences focusing on SAS) and frankly this season he's been inconsistent. He's been our main man but that's more of an indictment on our squad depth and form this year than a comment on how well he's played. If he was playing out of skin and had the consistency to back it up while the other players around him were playing poorly then I could understand but I personally reckon 2-3 players have been better than him this season (certainly since the change of formation).
I don't think he'll sign a new contract in the summer, and I think the club will absolutely look to sell him on. The only way I see him going to City is if they offer him silly money (very possible) as it's clear he's a London boy. I think the only possible way that he doesn't leave is if we win the FA Cup, and even then it's a stretch. I think it's pretty clear from the tone and timing of the interview that he's had his head turned and has no intention of signing the contract, but he's left enough ambiguity about it so that he's not completely burning his bridges.
It sounds a strange thing to say, but while I think it would be incredibly difficult to replace Sterling's raw talent and potential, I don't think it would be particularly difficult to replace his contribution to the team at present. Well, in theory it wouldn't be difficult, whether this club and transfer committee could manage it is an entirely different discussion.