As another comment points out, a lot of states do not require permits to purchase weapons. The cited article seems to rely on background check data. What about raw sales data?
This article from January 2016 shows total firearms sales rapidly increasing as of the end of 2015 -- did that trend suddenly collapse?
https://www.washingtonpost.com/news/wonk/wp/2016/01/05/gun-sales-hit-new-record-ahead-of-new-obama-gun-restrictions/
New federal data shows 2015 was a record-smashing year for the American firearms industry, with gun sales appearing to hit the highest level on record. Background checks for gun purchases and permits jumped 10 percent last year to 23.1 million, the largest number since the federal background check system began operating in 1998.
. . .
One point of caution with the FBI's numbers: The agency stresses that you can't draw a one-to-one correspondence between "background checks" and "gun sales." The numbers include background checks for gun permits, too, which may or may not be accompanied by a sale. Different states have different procedures in place for running permit checks, as The Washington Post's Philip Bump notes here. Some unknown but likely significant percentage of gun transactions don't involve a federally licensed dealer and hence aren't accompanied by a background check at all. (Obama's rules, which he formally announced Tuesday, would require more gun sellers to be licensed and conduct background checks.)
Still, the FBI's figures provide a useful approximation of overall gun transactions in this country. And they strongly indicate that 2015 was a great year for gun manufacturers.
One interesting wrinkle is that national surveys indicate that the number of households owning firearms is either flat or trending downward, depending on whether you prefer measurements by Gallup or the General Social Survey. If gun sales are increasing, as these numbers from the FBI and different data from the Bureau of Alcohol, Tobacco, Firearms and Explosives suggest, the implication is that most of the growth in the firearms industry is coming from existing owners stocking up on more guns, rather than new purchasers buying for the first time.