It's eating a flicker woodpecker. And yes, it did kill it and is eating it. Crows and ravens are omnivorous but also predators. They will opportunistically kill any small prey they can catch. Most birds are too quick for a crow, but flickers and all woodpeckers are notoriously slow flyers. It's about the only type of bird that is both small enough and slow enough for a crow to catch. Attached are some images of crows as predators.