Of course Goku would be good at a strategic battle game, what was Vegeta thinking! Obviously his pride got the better of him and he thought it would be an easy victory, though he did have the last laugh.
You did a great job of setting up the scene and telling it through Vegeta's eyes. Using a chess game was very creative, and I can see Goku teasing Vegeta like that very vividly from your narration.