The iteration of the Chessmaster series on the PlayStation 2 contains most of the features available in the corresponding PC game - which, in this case, is Chessmaster 9000. You can play training games (with all the hints and analysis tools available), rated games (your rating changes after each play), puzzles (chess ones, not the "build the picture" type), learn chess by browsing through the hundreds of tutorials available in the Pandolfini's Chess School or watch famous games.
There are, however, some new features in the PS2 version; the most useful one is the Online mode. Other is the "living world" of the Chessmaster Championships, where the AI's rating changes, too, as they play each other. The last one is more spectacular - a fantasy-themed - orcs vs. humans - game mode with animated chess sets and a 3D environment. You get to play chess in a forest, inside a castle and in the desert.