A Turing machine is a mathematical abstraction that represents a computer
It is commonly believed that a Turing machine can compute anything that is intuitively "computable", or in other words that a Turing machine is at least as "computationally powerful" as any other computer
So, if you can make a Turing machine using the game of Magic, certain results in math and computer science can now be applied to Magic itself
The most practical implication of this is that some game states are impossible to shortcut because you can't know how it will end without playing it out, and that playing it out can take effectively an arbitrarily long time