Q: Specifically, what do I need to do to run this program inside Emacs?
A: Copy each new code fragment into the Emacs scratch buffer (accessible via the command `C-x b *scratch*`) and move the cursor to the end of each expression and type the command `C-x C-e` to evaluate it.
To make a move in the game, you can just do exactly the same thing - The program will answer your move by displaying text in the echo area in the bottom of the Emacs window. If you did something wrong and Emacs starts showing error messages, you'll want to use the command `M-x top-level`... That usually clears out the errors.
One more thing: Sometimes Emacs will truncate messages in the echo area - run the following command in the `*scratch*` buffer to prevent this:

      (setq eval-expression-print-length nil)

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