Yup. The game has a single player mode and a battle mode where both gameplay systems are active. In Tetris, players make horizontal lines, but in Puyo Puyo vertical stacking tends to be the best strategy.
Famitsu reports Puyo Puyo Tetris is in development for PlayStation 3, PlayStation Vita, Nintendo 3DS, and Wii U. The game is slated for release in 2014.