No, you are incorrect. Kyle is not charged with an federal gun crime, and for good reason.
For a "straw man" purchase to be illegal, the gun has to be substantially transferred to the other person. The Smith & Wesson M15 was never substantially transferred to Kyle.
He is charged with two counts of the State crime in Wisconsin Statutes 948.60 2(a). But the judge dismissed the charge against Kyle (because of the exception in 948.60 3(c). The same exception exists for Dominick.
I never said Kyle was charged with making a straw man purchase. I said Black was charged.