For me, this was definitely an anti-war novel. How could it not be with multiple human lives destroyed forever by such senseless killings?
I also didn't consider it science fiction. Billy Pilgrim is escaping his demons the only way he knows - which is primarily through space travel- more indicative of PTSD than just fanciful thinking. Recently, a war veteran I knew (who was very young) took his life. On the outside he was a normal functioning father who worked to make a difference in the lives of teens with serious challenges. We will never know the 'why' but his published writing gives some clues as to the impact war has on the human mind.
Billy Pilgrim is a walking casualty who is coping to the best of his ability.
So it goes.