Maybe I'm biased, as I am an NRA member. But I think that side is much closer to outright fraud than it is parody, and probably should be taken down. I support good parody as much as anybody, but that site kinda dead-panned the delivery, if you know what I mean. It looks too serious and isn't necessarily immediately recognizable as parody and is harmful to the NRA's trademarks.
I think the video and website are pretty obviously parody. But, if you are having a hard time discerning it as parody, don't you think that's the NRA's fault?
I don't know. It's obviously a fuzzy line, and like I said, I am probably a little biased. OTOH, while I am an NRA member, they aren't my favorite gun-rights organization anyway. I prefer Gun Owners of America. shrug
Why the article ends with "censored by NRA"? NRA has all the rights to send a complaint because everybody does. And that's all they've done.
They do have the right to attempt to enforce their own trademarks. 37,999 of the sites taken down didn't infringe on the NRA's trademark, though, only one (allegedly) did. That's an overbroad exercise of trademark claim, a chilling effect, and arguably censorship.
It seems clear though, that those other sites being taken down was more of a misunderstanding / technical glitch, than any malicious activity by the NRA. And from the sounds of it, the other sites were restored relatively quickly.