Ah, I see. Sure, agreed.
Though I guess a lot depends on whether the computation* of Durham counting to 8 requires the computation of Durham being aware of having counted to 7. If it doesn't, then the program can produce the following sequence: x7 = Durham->countTo(7); x8 = Durham->countTo(8); Durham->awareOf(x8); Durham->awareOf(x7); with the result that Durham goes "8, 7" without any cheating.
The question of whether Durham experiences "7,8" or "8,7" is less clear, though.
With thanks to HonoreDB, yes, the structure must have a source. And also, as with the Chinese Room, there is a sleight-of-concept going on where something that looks like a human (Searle's paper manipulator and Egan's Durham) is not the actual "brains" of the system (which are really the symbol manipulation rules with Searle, or the dust/translator combination with Egan) that we're truly analyzing.
I agree with you that if there is not stateful process to worry about, but merely the instantiation of a trivially predictable "movie-like image ...
Permutation City is an awesome novel that was written in 1994. Even if the author, Greg Egan, used a caricature of this community as a bad guy in a more recent novel, his work is still a major influence on a lot of people around these parts who have read it. It dissolves so many questions around uploading and simulation that it's hard for someone who has read the book to talk about simulationist metaphysics without wanting to reference the novel... but doing that runs into constraints imposed by spoiler etiquette.
So go read Permutation City if you haven't read it already because it's philosophically important and a reasonably fun read.
In the meantime, if you haven't then you should also read A Fire Upon The Deep by Vernor Vinge (of "singularity" coining fame) and then read Eliezer's fan fic The Finale of the Ultimate Meta Mega Crossover which references both of them in interesting ways to make substantive philosophical points and doesn't take too long to read.
In the comments below there will be discussion that has spoilers for all three works.