If you've purchased a new computer, you can get WolfQuest: Anniversary Edition working with two steps:
1) Download the game again: This should happen automatically if you have the game from Steam. Otherwise, see these instructions.
2) Get your game saves etc. onto the new computer. If you have a WolfQuest game account, the game should automatically download all such files on your account, as they are synced to the WQ server every time you play the game.
But to be extra safe, you can also copy these files from your old computer to your new computer. To do this: Find the User Files folder (which contains your saved games, saved wolves, and screenshots) here:
Windows: Documents/My Games/Wolf Quest Anniversary/User Files/
Mac: [YourUserDirectory]/Wolf Quest Anniversary/User Files/
Move this folder (via local network or USB drive) into the same location on the new computer, then run the game, and your saved games and wolves should appear.