Now I was going to post some screenshots of the Pokédex's Aura Scan in action today, however... I got sidetracked (something that unfortunately happens too often).
So instead, here's some screenshots of one of the Game Corner's Pokémon Games:
The idea is to basically smash open each egg with super-effective hits from the Pokémon on the right. You do this by clicking on the Pokémon's attack you want to use, then repeatedly click on the egg until it cracks open, releasing the Pokémon inside. If the egg reaches the bottom of the screen, you lose a life.
Obviously it doesn't really make much real-life sense... but it's just supposed to be a bit of fun.
The Game Corner can be found in Raybourne Resort (check map up top) which is pretty much like a holiday destination in the region. There'll be quite a few mini-games, where getting really high-scores can bag you some rare Pokémon - though be prepared to spend some money trying.