A proper turing machine has an infinite amount of accessible storage. A "turing complete" computer today generally operates with a finite amount of accessible storage, and we mean that it is able to compute operations that use less than that finite amount of accessible storage - not that an infinite number of resources are available.

As best I understand it, the Antikythera mechanism has only a few stored values, and makes only addition and subtraction computations from them to give various outputs. In that sense, it's accessible storage is about 3 floating point numbers, and it is not turing complete within that storage domain, because it cannot divide, take square roots, and do other things possible in that size.

It would almost certainly get stuck when Steam tries to precompute the Vulkan shaders.