A lot of emphasis is placed on the White Phosphorous scene, and whilst it is one of the game's two turning points, there is more to it than just that scene. The game sets you off with an objective, namely "go into Dubai, see if anyone's still alive in there, and then bug out and let us know if you find anyone who needs evacuation and we'll send in something more substantial than three guys".
You get your answer about 10 minutes in, you find some Arabs, and since it's a game you shoot them all. You find that they've been killing other American soldiers, so of course you shoot more of them. It's a game where you're an American soldier and there are some dirty foreigners, same as everything else so far.
Then they swap out the foreign people for American soldiers. You'll be shooting at them now. The game makes this swap about an hour in, when you're still thinking "oh, it's just another military shooter, I don't care who I'm shooting, I just want to shoot people".
Then they reveal that the American soldiers are rounding up civilians to be evacuated. The people you're shooting are actually trying to help people. You're still in "another military shooter" mode, so you don't care. Your character, Captain Walker, makes up John Konrad, who he then starts blaming for everything he's done wrong. Walker hallucinates a series of radio messages from Konrad, taunting him. You're not told that Konrad is dead, and that the radio messages are hallucinations, the player is just told that Konrad is evil and he should die.
And THEN the White Phosphorous scene happens. Just as the player says "I didn't kill those people, it's the game's fault", Walker says "No, this isn't my fault, this is all Konrad's fault, let's find him and kill him". Then Walker's character shifts. His voice stabs change from "Focus fire on my target" to "KILL HIM!". Rather than killing wounded enemies with a swift bullet between the eyes, he starts to torture them a little, he'll shoot them in the kneecap to let them squirm before taking their head off. From the player's point of view, they're still doing the same things - running up to a wounded enemy and pressing shift to kill them. From Walker's point of view, he's still doing the same thing, he's taking soldiers that are wounded in battle and putting them out of their misery. But we know that something's changed, the camera's focused more on the victim than on the killer, and the game isn't congratulating the player for scoring some good kills, it's making the player out to be a murderer.
You continue regardless, because you've got an objective to complete; find Konrad and kill him, because you didn't choose to do any of those things, Konrad did it. You find another man who tells you that he can take you to Konrad in return for a favour; help him steal Dubai's water supply. The game tells you to destabilise an entire city, and so you do. Walker rationalises everything by saying "no, not my idea, not my choice, I can't exactly turn back, so I'll help this guy". So on you go, the game tells you "destroy the water supply - this will kill everyone in Dubai", and the player, absolved of responsibility, heads out and does just that.
This post's getting awfully long, so I'm going to fast forward a little - a squadmate dies, you besiege an american military encampment, and then you actually reach your goal. You enter the tallest tower in Dubai, and John Konrad reveals himself. He's painted a picture of the White Phosphorous scene, and he asks you about it. "How do you think it looks?" "No, I didn't do this, you did." That line right there is said both to the player and to Captain Walker. By this point, most players had forgotten the original objective. You're told "You're here because you wanted to feel like something you're not - a hero". How heroic does the player normally feel at the end of a game? You're told, "well done, you saved the world, you're the best thing in the universe!". Even in the "bad" ending of Dishonored, Emily tells you right at the end "You're my hero Corvo!". Spec Ops doesn't have a "good" ending, it asks you just how heroic you feel for murdering an entire city full of people, and it does so straight-faced, and then gives you a simple question.
"Can you still live with yourself?"
Your hallucination of Konrad walks you over to his dead body, slumped in a chair holding a gun, having shot himself through the head a very long time ago. The secrets are finally revealed, you learn that there is no Konrad, and that Walker has been shifting the blame for his actions onto someone who doesn't exist, just as the player has been blaming the game for the things that they've done. Walker picks up the gun, and is given a choice. Walker and Konrad's illusion walk over to a mirror, Konrad pulls out a gun and points it at Walker saying "I'm going to count to 5, then I'm pulling the trigger. If you think this is really my fault then shoot me", and the game switches back from cutscene mode to third person shooter mode. You and Konrad are in front of a mirror, so you can see your own reflection, as well as Konrad's illusion. Using exactly the same mechanics as you used to kill every other person in the game, you use the mouse to aim the gun either at a man who doesn't exist, or at yourself, then left click to pull the trigger.
The suicide is probably the most powerful thing I've seen a game do:
Watch the video and listen out for the double-lines, said to Walker but meant for the player.
Reading about the game can't do it justice, but it's a powerful, demanding, and beautifully crafted experience for people who really want to explore how well a game can tell a story and make a point.