When a corporate or person's name/trademark is used explicitly and intentionally, freedom of speech does not automatically inherently protect the publication or media. In such a case, damages (if any) are resolved on a case-by-case basis, generally depending on the content and how indistinguishable it is from the real thing (and whether it's potentially damaging).
Saturday Night Live and The Onion are protected because both are widely known and clearly labeled as comedy/satire content. Neither is the case for this video, and as a result it's extremely likely they would fail at defending a lawsuit from the NRA if they did decide to prosecute.
P.S. My post assumed nothing about anyone's political views. The planned parenthood example was meant to provide balance via an analogical example from the other stereotypical political side.