I believe you have misunderstood what I have said. My issue with Magic was not with the logic specifically. It is with the fact that it requires the player to initiate state transition by specifically selecting actions. It would be permissible if the player simply functioned as a clock, but some of the state transition logic is actually shifted over to the player. It certainly is better than the pen and paper scenario, but the rule system is incomplete. It still requires a couple of rules for the player to follow (just as pen/paper or an abacus does).

The author mentions this problem explicitly on the "Difficulties" section of the site. It is very important to note this. The hope is for the effects of some cards to allow for the necessary computational depth to capture all of computation without additional human action (besides, lets say, initialization). People often look at Turing Machines and their components. They forget to think about state transitions and the recursion involved (recursion really is the "meat" of computation).