Baek Doo San was the South Korean Tae Kwon Do fighter who debuted as Marshall Law's sub-boss in Tekken 2.
Baek's story explains the matchup: during a sparring session, he accidentally killed his father. Overcome with rage and grief, Baek went on a destructive rampage and attacked several martial-arts dojos, including Marshall Law's. Law therefore entered the second King of Iron Fist Tournament seeking revenge for the destruction of his dojo.
In arcade mode, Baek is associated with Law as his character-specific sub-boss. This is also Baek's first appearance in the series. His fighting style is Tae Kwon Do, distinguishing him from Law's Jeet Kune Do-inspired moveset and from the other options listed in the question.
Baek later became closely connected to Hwoarang, serving as his mentor. That later relationship can cause confusion, because Hwoarang is also a Korean Tae Kwon Do fighter and Baek's pupil, but Hwoarang did not debut as Law's Tekken 2 sub-boss.