How do NFA's make program design any better when converted DFA form can't remember original states? Here is some content from the book by Peter-Linz I read

&quot;Consider a game-playing program where the machine needs to make the decision for the next move [say for tic-tac-toe]. Since there are multiple moves possible, we deterministically choose each move and evaluate the move and opt for the best one. Even though the selection process was deterministic and there were many possible moves, the final move made was a single one and was chose as best move while hiding all the tried move-computations from the opponent. [Here we assume that the evaluation process of each possible move was hidden from the opponent].
Hence only one choice was made and opponent is given a illusion such that the move was non-deterministic.&quot;

My question is: if an NFA is translated to a DFA for implementation purpose ,how does the DFA make(remember) the correct transitions to the states defined in the original NFA(the game)? My confusion stems from the fact that when an NFA is translated to an DFA it's states get mixed up.
Suppose in a simple game below ,Player is at center position and he wins if he moves leftwards:

if the above DFA is implemented it surely finds a winning state on a &quot;m&quot;(move),but how does it decide whether it was right or left move?
[i]f the above DFA is implemented it surely finds a winning state on a "m"(move),but how does it decide whether it was right or left move?


In the example you gave, it can't. The nondeterministic transition from the start state occurs when a "move" is made. That's all you can possibly know; the machine can't determine whether the winning move was left or right, because those aren't allowed possibilities.