Joxer

I've noticed with several xbox 360 games that it lists it's multiplayer as "online" Which means that each person who wishes to play the game needs to purchase the game and play it on their own console. I am currently looking for some fun games for me and my girlfriend to play, so I need them to be multiplayer "on the same console". I've seen people playing 3D Ultra Minigolf in groups on youtube, but again, when I went to check it out on the store it says "Multiplayer: online". Has anyone purchased this game? Can you do multiplayer on the same console, or does each person have to buy the game?