The loop unrolling is an implementation detail. As I have written somewhere else: You could as well have put a large if-else there to do the transition table lookup.

In the GoL example, one generation update is performed in every transaction. Since the board size is known in advance, it totally makes sense to unroll the loop. If you want to do boards larger than that, like the 1000x1000 you mention, you run into script limits. What you can then do instead is, for example, to update the first half of the board in one transaction and then the second half in another transaction, i.e. two transactions are one generation.

Bitcoin is turing complete as shown in this article.