Many Atheists and Agnostics believe that if God did exist, he wouldn't actually play an active role in human affairs. There is something to say for that viewpoint, considering the lack of fate or control present in our day-to-day lives, and how feasibly a morally good, benevolent person wouldn't just sit and watch while the people he/she cares about suffer. Or one could argue that God doesn't intervene with humanity because it believes that free will is more important for the human race. Given Alan Moore's spirituality, he may believe in spiritual forces in our world, but it's highly unlikely that he belives in an authoritarian God that actively controls what we say and do. And his portrayal of Dr. Manhattan doesn't dispute this.
This view is best demonstrated in Chapter 2, where Dr. Manhattan just watches while The Comedian guns down his pregnant Vietnamese girlfriend. The Comedian tells Dr. Manhattan that if he really wanted to save that woman and her baby, then he could have "turned the bullets into mercury, turned the gun into snowflakes or teleported either of them to goddamn Australia". But he didn't, because he no longer cared about the suffering of humanity.
Basically Dr. Manhattan represented God, and The Comedian gunning down his pregnant girlfriend represented the suffering of humanity.
But when stacked against Jon Osterman (Doctor Manhattan's powers, he's no more a threat than the smartest termite. A man of Adrian's arrogance wouldn't take that lying down. He's envious of Manhattan's natural power over the universe, and tries to replicate it for himself. His TV wall is a prime example. Dozens of television sets, each tuned in to a different channel, in an effort to see everywhere in the world at once, and determine the best course of action. He wants to be all-seeing, and works hard to be that way.
But Doctor Manhattan just is that way. He not only sees everywhere in the world at once, but he all of time. Past, present, and future are all one for him. No special equipment required.
In the final scene, Adrian tries to justify himself to Jon in an orrery. A small model of the solar system is set in the middle, constellations on the walls, a light bulb functioning as the sun in the center. Overseeing the model is a meditating Adrian Veidt, looking intentionally godly. He says that he forced himself to feel the weight of the sacrifice, casting himself as the necessary savior.
But then, Jon walks through the walls, into the model, turning the orange light to blue, casually ponders going to another galaxy to create life there, poses like Da Vinci's Vitruvian Man, while this faux cosmos revolves around him, exposing Adrian's self-doubt.
Doctor Manhattan is the only character to defeat Adrian. How? By breaking him with the truth. Adrian tries so desperately to be a modern demigod. Jon just is one, and it drives him insane. The constant reminder that, for all his success and achievements, he is merely mortal.