Custom Post Loop pulling all custom posts, not just one

You are within the loop already. You don’t need to recreate it (by making another WP_Query). Here is your code, with the $loop you created removed. This should work perfectly.

<?php /*Template Name: Game Listing Page */ ?>
<?php get_header(); ?>

<div id="content">
    <?php while ( have_posts() ) : the_post();?>
        <article id="post-<?php the_ID(); ?>" <?php post_class(); ?>>
            <header class="entry-header">

                <!-- Display featured image in right-aligned floating div -->
                <div style="float: right; margin: 10px">
                    <?php the_post_thumbnail( array( 100, 100 ) ); ?>
                </div>

                <!-- Display game information and review score -->
                <strong>Title: </strong><?php the_title(); ?><br />
                <strong>Platform(s): </strong>
                <?php the_terms( $post->ID, 'games_database_game_platform' ,  ' ' ); ?>
                <br />
                <strong>Genre: </strong>
                <?php the_terms( $post->ID, 'games_database_game_genre' ,  ' ' ); ?>
                <br />
                <strong>Publisher: </strong>
                <?php echo esc_html( get_post_meta( get_the_ID(), 'game_publisher', true ) ); ?>
                <br />
                <strong>Developer: </strong>
                <?php echo esc_html( get_post_meta( get_the_ID(), 'game_developer', true ) ); ?>
                <br />
                <strong>Review Score: </strong>
                <?php echo esc_html( get_post_meta( get_the_ID(), 'game_rating', true ) ); ?>
                <br />

            </header>

            <!-- Display movie review contents -->
            <div class="entry-content"><?php the_content(); ?></div>
        </article>

    <?php endwhile; ?>
    </div>
</div>

<?php get_sidebar(); ?>
<?php get_footer(); ?>