It ain't Chessmaster.
The game is only $2.99 so it's not going to break you, but you should have a rough idea of what you're getting.
The game has three modes - quick single player, two player and 24 chess puzzles. There's also a tutorial mode.
For the single player you have a choice of 6 opponents. The highest setting did not seem difficult, not like the highest setting in Chessmaster. I think if you're a big chess fan, you won't find much of a challenge here.
A free chess game on the PC called NagaSkaki chess provides a better challenge and I recommend that game if you haven't tried it yet.
What I didn't like is that every time you select a piece to move, the available moves are shown in green - you can't turn this off and I found it annoying. Minor but still annoying.
The game really only uses half of the game screen. Half is the board and the other half is a picture of your opponent. The opponent's face sometimes changes but to me it's a waste. They should have used the space to show what pieces from the board have been taken. Hell, I would have settled for a picture of a waterfall than a odd looking cartoon character's face.
Chessmaster The Art of Learning on the NDS blows this game out of the water, but if you don't have a NDS or want a cheap but functional chess game on your PSP or PS3, for three bucks its just okay.