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The spirit of the law was that handguns should be on the NFA, and SBRs needed to be too so people can’t cut a rifle to handgun size to circumvent the handgun restriction. But handguns got taken out, and we’re left with this nonsensical mess.
Im going out on a limb here and will say that I don't think the approach here is dumb, but that the quagmire of rules, rights and regulations can only result in weird and strange rules in the end. 
I can see why the ATF would want to close the loophole for pistol braces, especially since they are such a blatant way of breaking the spirit of the law while technically being inside it. You even mentioned how they marketing itself acknowledges this. Personally I have never seen anybody actually using a pistol brace for its intended use either online or in person before I saw your linked picture.
Anyway: They want to change those rules. They can't just outright ban them, because the ATF can't make new laws and there is nothing unlawful about pistol braces. Besides there are actually some who needs them for their intended purpose.
This means they have to find another way to regulate them. And SBR's are where pistol braces are most widely used so it makes sense to go at it from that angle. So the ATF deems: "All pistol stabilising braces are now rifle stocks". This is pretty nifty as it accomplishes two things. 1: Now a lot of "pistols" are now SBR's unless they adhere to the two pages with 8 questions you linked to and has to be regulated through tax stamps 2. People who needs a pistol brace are no longer discriminated against and can use them for their intended use.
Now I won't go into the whole "tax stamp" thing because frankly it is such an odd concept to me and besides I can't understand people who are willing to spend hundreds or even thousands for a SBR only to try to skirt the law to save $200. But that is besides the point. For some weird reason people have to pay this tax for a SBR and the ATF are the ones who apparently can define what a SBR is.
But the end result is that if people has to pay a tax stamp to have a stock anyway then they will chose a proper one and not one that is slightly-less-than-ideal, meaning that pistol braces will slowly only be used for their original purpose. Problems regarding pistol braces are now solved according to the ATF.
So while the end result might be confusing their approach makes a lot of sense imo. 
Caveat: Im not from the US, so my view on gun laws and gun culture might not be 100% up to date.