As I understand it, the argument seems to be Aha! Church-Turing Thesis applies to functions, but interactive systems aren't functions, take that Alan and Alonzo.
Which is one of (a) an attack on a ludicrous straw-man, (b) true but not interesting or (c) quite profound or at any rate slightly sneaky. I am not sure which. Off the top of my head I am surprised that this isn't a popular attack on hard AI.
'You may be appealing to the Church-Turing Thesis, but that refers to mathematical functions. The real world is not clearly quantized in time and space, therefore rather than a function from Z to Z, interacting with the world is a mapping from R, so your thesis is no match for my real numbers and I therefore contend that my wibbly-wobbly brainy-wainy stuff has magic powers. Or at any rate that you can't appeal to that nice Dr. Turing.'
Or am I missing something?
Obviously you could define some sort of Turing machine where bits of the tape get values from the outside world and compare it to a Universal Register Machine with interrupts etc. and prove their equivalence.
Or you could walk the dog.