Dear Friend,
You ask why did God order the killing of all living creatures in 1 Samuel 15:3. You asked in response to why Richard Dawkins blames God for evil but does not like it when God wipes out evil in the Old Testament.
My answer to you is read the whole chapter & you will see that the Amelak opposed Israel as they sojourned out of Egypt. As their King God has responsibility to defend His chosen people. But they wanted a human king so God gave them Saul. Yet Saul was disobedient to God thinking only of himself keeping stuff for himself not obedient to God's word. (Dt. 20:16, 18) War making for Saul was making a profit. The law of Moses prohibited warring for gain.
You sit in judgment of God. Who are you to do so? You walk on his earth, breath his air and like Saul claim for yourself faculties such as reason and you use them for your own purpose. The land was promised to Israel. The Alemakites were trespassers. Who among us would not call the police to remove a trespasser from our home. If they resisted they may be shot. Out of Israel a Messiah came, Jesus of Nazareth. He gave himself as a perfect sacrificial lamb so that we may enter into God's presence, evil though we are. Yet by turning away from our sins & accepting Jesus as Lord, we will be given a new heart. We become a new creation putting away our evil self by God's help. Our eyes are opened to our sinful nature. We see what we are really like. Everyday when you wake up you need to thank God for His mercies. For the rain & sunshine, for the food on your table. You created none of these but you consume them without saying thank you. You go about your business taking the Lord's Name in vain. How many of you ever use your mother's name as a cuss word? Your happy to deny truth. Your happy lying to protect yourself. What should your judgment be at death. Truly, this is God's earth, He made it and all that is in it. He can do whatever He pleases. He does not need our approval. We on the other hand need to recognize our horrid state & bow down before Him asking mercy to spare our life. This is no mere philosophical notion, as Jesus died in our place taking upon Himself God’s wrath meant for us. Think about it & repent!
God showed His love us that while we are still sinners, Christ died for us! (Rm. 5:8)