RPG, Final Fantasy 10, 12, remakes of DQ8 and 6, Xinghai Legend and Nanmeng Palace Legend Series. Twilight of non-mainstream elves is also good (one of the few official games in China). I can't speak Japanese, and there aren't many RPGs in Chinese on ps2. I basically know all this.
Strategy game has always been a niche game. It seems that there are only Glorious Three Kingdoms series and Xinwu Wangye series on ps2, and Chen Uen Three Kingdoms in Taiwan Province can also be played. If you count the war chess, there are more, such as computer war series, summoning night series, Wrist of Tears Legend 2.
PS: Actually, the most classic games on ps2 are those action games.