Well, it's not strictly necessary. The anime might give you a decent overview. But the manga often has more details and might offer a different perspective.
The basic structure of the story is also alike in the manga and the novel of 'All You Need Is Kill'. There is an introduction to the world and the situation, the main character's initial struggle within the time - loop, and then the progression towards finding a solution to break the loop. This common structure helps to keep the essence of the story consistent across the two different forms of media.