Humanity only answers for sin to one person. God is our Judge. That is made clear in this passage. The scope of this pronouncement of judgment seems much broader than just the ruthlessness of Babylon. God is taking the step of proclaiming punishment for the entire world. So there is a lot more going on here.
God takes responsibility for being the only Judge of mankind. He does not do so in any other way than in absolute holiness. But the fact is, sin is dealt with by holy judgment. Nobody gets a free pass on this. And the worst societal sins (in the context typified by the brutal conquests and pride of Babylon) will receive a thorough judgment in the work of God in the world. Sin will be met with justice.
When we see a "problem" with God's right to judge, the problem we see is ours and not God's. It is part of the sinful perversity of human pride to think our sins do not really merit judgment from a holy God. But we are sinning with that line of thinking. We want to make ourselves higher than God. We must accept God's absolute moral authority to judge sin-filled humanity.
Christians look back on passages like this through the redemptive history that culminated in Jesus' salvation for us at Calvary. There all sin was atoned for so that judgment was borne for all who believe. And the gospel overcomes the eternal results of God's judgment. It provided a way out for those who will come to Jesus and learn to follow Him. A holy God provided redemption AND judges sin all in Jesus. We cannot forget that. The gospel is our perspective on judgment. It is Good News for a world under condemnation.