Death threats are just as valid online (or at least are in many places) as they are in the physical world. There is a difference in terms of whether the threat is genuine or not; if one anonymous person threatens another anonymous person - can it really be believed that the threat is credible despite its obviously impractical nature?

Just like in the real world, the venue is not responsible. Walmart is not responsible if someone shouts death threats inside. Walmart or other users/customers can call the police but it's not Walmart's job to tackle the guy. The really only difference is that local & state law enforcement is less inclined to enforce the law against online individuals given the time & energy required in addition the the threat being significantly less likely to be credible.