One of my pastors once pointed out that when Jesus died and was resurrected it was almost as if he pulled the entire world through the cross leaving it a new and resurrected reality on the other side. I find this to be a poignant and profound image. While the world is stil very broken and in need of redemption, the world after Christ is different than the world before Christ. On this side of the cross, in places where the gospel has penetrated, it can be taken as a given that God is one who does not delight in wickedness. The whole notion of the philosophical debate about the "problem of evil," or theodicy, is premised on this. But before the cross we had the Molech's, the Baal's, the Greco-Roman pantheon that delighted in wickedness of all manner. So we should not just gloss over such statements. It is not a given. We should give thanks that we know the true God, the God who does not delight in wickedness but in grace, mercy and love.
At the same time, reading on in the Psalm, we should remember that God delights to bless the righteous and humble the wicked. We should never be self-righteous, but neither should we engage in false humility. David is not afraid to pray that God would bless him for his righteousness/faithfulness and cast down/destroy the wicked. In our day it is fashionable to assume that there is some sort of neutrality whereby the righteous and wicked can peacefully co-exist (and the righteous aren't really righteous anyway because we are all depraved). However, David will have none of this. Living on the backside of the resurrection he has a full appreciation of the death and destruction that wickedness leads to, and while we know from his other Psalms and the historical books that he certainly would prefer to see the enemies of God converted rather than destroyed, he is not afraid to contrast his own faithfulness to the Lord with their murderousness and implore the Lord to bring destruction on them and remember his faithfulness.
This is not somehow sub-Christian. The Psalter is the Christian's hymnbook. We should simultaneously recognize God's grace and his disgust at wickedness. We should praise him for his holiness, thank him for his grace, pray for our enemies, and at the same time pray that he would destroy those who seek to do his people and his kingdom harm. God is not a genie in a bottle. You don't have three wishes and then it's over. You can ask him to convert your enemies, bless you and the other righteous (and yes it is okay to number yourselves among the righteous, otherwise you can't pray/sing the Psalms), bring the kingdom, and destroy those who delight in wicked. God can sort out the details. He knows that some of these requests feel mutually exclusive, yet he exhorts you to make each of them.
So thank God that you live in a world where the statement 'God does not delight in wickedness' is tautological, ask him to remember you, bless your faithfulness, build the kingdom, convert its enemies, and destroy those who love wickedness. And trust him to work it out.