Spree is neither negative nor positive, it only means you are doing a lot of something, or over a long period of time. There are shooting sprees, crime sprees, shopping sprees, gaming sprees, etc. So in this context, the worst shooting spree in U.S. history, means the man shot more people in one event than anyone else in U.S. He did a lot of shooting, so its a spree.

To go on 'a shooting spree' means to shoot randomly and very, very much. Another phrase for this would be: To go on a shooting rampage.