Zookeeper originally was an innovative puzzle game that added new things to the casual puzzle mix and now, we have online multiplayer with players around the world but we had to sacrifice some things to get it. Battling players around the world, even in different languages is pretty awesome (this is achieved through only offering pre-selected greetings).
Matching animals up in sets of three or more is the key here. Zookeeper goes one step farther though, each animal is imbued with special abilities, some will heal your avatar in battle while others will attack your opponent and some have both capabilities available. This adds a ton of strategy to the battles but still, a lot of left to chance and sheer luck.
Each round is 30 seconds long, match as many animals as possible in that time and then you slug it out with your opponent. If either side runs out of energy they loose, fairly simple. If after five rounds there is a draw then the winner is decided based on the amount of energy left.
Bejeweled fans looking for something that is online and even more addictive should check out Zookeeper Battle. It is worth money but they are giving it away for free.