In North America, Palamedes was made by Hot-B! I knew those two companies had a small relationship... or something.
The Tournament Game is the single-player versus mode, where you can play against a CPU, in a small number of stages. "VS Game" is the mode where you can play human vs. human. In a versus game, clearing lines on one side will send more lines to the other. The loser is the first to get the general game over situation.