I would not expect computers and/or computer science to improve the performance of students in SAT Mathematics, AP Calculus, and AP Statistics.
We use computers so we dont have to remember all that crap. The computer does the math.
I would expect it to improve reading, reading comprehension, written language skills, and logical thinking. That is what the student is learning!
Computing teaches any problem domain that you are asked to code solutions for.
The problem with initiatives like code.org is that they generally try to engage kids by making things move on the screen. Most of that means doing very basic arithmetic in an esoteric firmat surrounded by Byzantine library calls.
If you want kids to do better in statistics, you shouldn't start with the paradigm of interactive entertainment, but with the far less abstract view of a computer as something that computes stuff. Kids might not like their schoolwork, but it's certainly relevant to them. Part of the problem teaching complex maths is that the mechanics of carrying out the underlying computations diverts attention from the "big picture" view. Procedural computing was designed specifically to address the problem of "can't see the wood for the trees" by separating the general algorithm from the specifics of implementation.
I think they are conflating programming and computer science. I think theres a lot of this confusion surrounding the discussion of this article, and indeed in teaching computer science at this level.
Computer science is only tangentially related to programming.
Most of computer science involves things like logic and discrete maths; state machines, turing machines, computation theory, set theory, algebra of functions, big-O notation and efficiency of algorithms. I majored in computer science and did very little actual programming. In fact I hated programming, still do. I can't comprehend people who program 'for fun'. But I did enjoy delving into the math that lurks beneath computing, discovering the limitations of algorithms (and hence of any methodical approach to a problem ie there are some problems that no computational process can solve, not because they are NP hard, its worse than that). Computer science introduced me to things like Chaitins algorithmic information theory and the first known uncomputable number (the halting probability), Goedels incompleteness theorem etc.