This is the part where the second section of that structure comes in. Now he turns to talking directly to God, and he declares here in the first line that he understands that God is the only one with true power. That makes a big difference. His enemies thought they had power. They thought that they could overthrow David. They thought that if they did their conspiracy or their whisper campaign or whatever that they could take him off the throne and replace him. But David dispels that. He says, "No. The only real power in this world is God. He alone has true sovereignty."
And then he goes on in verse 12 to show that one of the ways He shows His power most obviously in the world is through His judgment, through His position as righteous Judge. So He renders to one justice and to another mercy. The word here is chesed, that lovingkindness, that covenant love, and he is showing that there are two sides. God shows His power on the one hand against those who deserve justice because of the way they treated their fellow man, or specifically in this case, he is talking about how they treated David. But on the other hand, He also uses His judgment to show mercy, kindness, love, to those whose side He is on—because they are on His side and they are working together in this covenant relationship.
And so, what you get out of these two verses is that David is saying, "Look, God holds all the cards. Just get that through your thick skull. God is the one with all the power even though the people out in the world don't think that it's the truth. It's reality that God is the only legitimate power. Power belongs to Him. He has it and He could give it or withhold it at His discretion."