Your statement and the headline are grammatically equivalent (minus your comma). However, the sentence is strange because “by” implies a causation that is not supported between the supposed cause and the supposed effect. The Neanderthals were brought to the cave to be eaten; it’s almost but not quite backwards.

My guess is what the author means is, “By preying upon...” which would be correct because dragging them to the cave is part of their predation. “By eating them” implies they were eaten and then, because of the eating, wound up in the cave (say through defecation or inside the stomachs of dead hyenas).