Turing-complete means it's capable of expressing any possible program, although it only looks at the pure logic, it doesn't look at timing constraints or resource constraints.

So, the redstone simulation would definitely be too slow to create an actually playable version of Minecraft, and there's almost certainly other simulation limits you would hit, like e.g. the redstone not fitting into the area the game actually computes, but in principle, you could express all the same logic.