Those two examples above are just two of the many types of game engines out there. Game engines are the foundations that allow you to run the game. 3Ds Max is a 3d package that you can use to create the 'stuff' to put within the engine. The engine gives you the ability to move around your assets that you have imported from 3ds max or other 3d packages.
But you can't just import objects and think everything is going to work, as I found myself with quite a slap in the face. You have to add collision messes; these are invisible geometric shapes that are set around the assets to stop you from walking through them. Have you ever played a game where you have gotten stuck between two objects but you can see a gap that you could actually go through. Well that's the collision mesh. (annoying buggers, but they do have a very good purpose).
Such a beautifully made game. I like the stylelisation and the colour palette through out.
My other brother got an xbox kinect from Santa... After trying it out for the first time, I am very impressed with the outcome of it and the games available for it. It is very clever how it recognises you the player and how you interect with any of the games (Fruit Ninja has given hours of fun, especially for a game that started off as an app for the iphone).
The game that you get with the Kinect, Kinect Adventures was also made using UDK. I found that quite impressive for the type of game that it is, simply because of the amount of player movement required in the game.