This is just a miscommunication of what "better" means in this context.

No one disputes that a modern computer implementing a Turing machine is going to calculate faster than manually manipulating MTG cards.

However, better here means 'more expressive'. Turing completeness is concerned with whether or not a computational system is 'universal' or not. In other words, whether that computational system can compute everything that another computational system could. If two systems can both be shown to simulate a Turing machine, then that means that those systems could compute the same exact set of things (given enough time).

So with regards to expressiveness (or the things a system could theoretically compute), since a modern computer can implement a Turing machine and a MTG game can implement a Turing machine, they are both the same, and thus neither is 'better'. In other words, the addition of electricity doesn't effect what a system could theoretically compute.