Supremes rule in US v. Stevens
Opinion in pdf here. At issue was 18 U. S. C. §48, which outlaws the commercial creation, sale, or possession of videos or other depictions," in which “a living animal is intentionally maimed, mutilated, tortured, wounded, or killed,” if that conduct violates the law where “the creation, sale, or possession takes place.” As the 8 person majority noted, this would include hunting and humane killing (since the prohibition on "wounded or killed" is separate from the ones on maiming, etc.. It is also evident that this would apply even if the hunting were legal where filmed, since the ban kicks in if the filmed activity is illegal where possessed or viewed, so hunting is included then a video of it would be illegal to possess anywhere in which that form of hunting isn't allowed. NRA, SCI, and others had intervened to point this out.
There was an exemption for depictions with “serious religious, political, scientific, educational, journalistic, historical, or artistic value.” The dissenter (Justice Alito) maintained that hunting videos would be protected by it, but the majority notes (1) it requires "serious" value, leaving a person to guess how serious is serious and (2) the list doesn't include simple entertainment, and it's unclear that hunting would fit under religious, political, scientific, etc..