Why can't I play a downloaded game on XBox 360?

My brother had downloaded several games onto our old console such as GTA 4, Minecraft and a bunch of other ones through his XBox Live account. That console wasn't working so good so we bought another console. He transfered his XBox Live account to the new console and I had to make a new profile on the new console. He redownloaded all the games from the old console into the new console. He can play those games just fine and he has no problems. However, when I try to play those games, it always gives me a message saying that the game won't launch. We theorized that it is because he bought the games on his account so only he can play it. However, when we had our old console, I was able to play those games without a problem. Can anybody give me some advice or anything about what could be the problem and the solution?