This is totally not obvious, and hard to figure out (or find on the Google), so I thought I'd share. One of the nice things about Windows RT is that it is still Windows, so you can set up user accounts on your tablet. That means each user can set up live tiles and arrange them to their taste.
Buying stuff, like Angry Birds Space, ties the app to your store account, so by default, other users won't see your apps on the same machine. To allow them to be used by others, you have to go into the store settings on their account, and change the sign-in to yours. Then go into the store, swipe in from the top (or right-click) and choose my apps, and install the apps that you've already purchased.
By the way, this works across machines as well, so you can install the same apps on your desktop, for example.