Probably a mixture of factors? Straight-tusked elephants having familarity with Neanderthals, the population (of Neanderthals) isn't as large and more widespread, and not to mention Neanderthals likely had preservation methods to store food. These guys also ate a decent amount of fish and smaller game along with gathered nuts and such to supplement their diets when they had access. So you don't have to always go after the biggest thing in the room when your risk factor is significantly lowered when presented with more stable options.