Bearing similarity to Puzzle Quest, Neopets Puzzle Adventure is a role playing game where the battles take the form of a game of Reversi.
You and your opponent take turns placing tokens on the board. You capture your opponent's tokens by placing your tokens on either side of a straight line of your opponent's tokens. You win by either eliminating all your opponent's tokens, by keeping him from capturing anything for 3 moves, or by having more points when the board is filled.
The RPG aspects take the form of stats, which can increase your points, and equipment, items, and petpets, which let you do otherwise illegal moves a limited number of times in each battle, or manipulate point totals. Outside of battle, you can take on quests, talk to people, fight and capture petpets, and shop.
In the story, you're busy helping the crew of the Cyodrake's Gaze when the city you're in is attacked in pursuit of an amulet that soon ends up in your possession. Now it's up to you to figure out what it does and who's after it before it's too late.