Mortal Kombat: Deadly Alliance's Konquest mode reveals that master Bo' Rai Cho helped Muso develop the style, and that he actually won the second match. Unfortunately, it also claims that Muso later lost to Shang Tsung.
Bo' Rai Cho uses Jojutsu as his weapon fighting style in all of his appearances throughout the series, in Mortal Kombat: Deadly Alliance, Deception, Unchained and Armageddon. He also uses the weapon again in his Bartitsu Variation.
"Jojutsu is the Japanese art of the short staff. It was first used by Muso Gonnosuke in the early 1600's after his loss to the swordsman, Miyamato Musashi, while using a long staff of 6 feet. With assistance from Master Bo' Rai Cho, he subsequently developed a style with a shorter staff of 4 feet. Although he beat Musashi in a second duel, he was later defeated in his first Mortal Kombat tournament. Gonnosuke's soul was consumed by the sorcerer Shang Tsung."