We got reported that the Hangman game was not respecting the attempt limit when a student finished the game. The problem was that, when a student finished all its attempts it reloaded the page so it gets a brand new attempt.
To correct this problem (just for the Hangman game) we added a this code at the mod/game/attempt.php file, in the game_do_attempt() function and before the if ($continue) statement:

    if ($game->gamekind == "hangman") {

        global $USER, $CFG;

        $unfinishedattempt = game_get_user_attempt_unfinished($game->id, $USER->id);

        if ((!$unfinishedattempt) && (!game_can_start_new_attempt($game))) {

            $continue = false;

            $redirect_url = $CFG->wwwroot . '/mod/game/view.php?id=' . $cm->id;

            redirect($redirect_url);

        }

    }

Our current Moodle version is 3.9.4