That's not a valid game state. It's like saying chess is Touring complete when played on an infinite board.

By this argument, x84_64 assembly isn't Turing complete because it needs finite memory...

Which is technically correct, just not very useful.

My Philosophy of Computer Science professor argued that you could prove anything was Turing complete, by suitably "gerrymandering the inputs" of your definition.

What that actually means, I'm not sure. I know how gerrymandered congress is, and they couldn't possibly get enough work done to be Turing complete.

That's what I've ment, it's not 'Magic the Game' but inventing rules [1] for magic card handling that represents a Turing machine.

[1] "A Rotlung Reanimator makes a messenger token for Alex."