That man was one of The Joker's many Goons. He was never seen with the rest of his gang. His appearance was ambiguous: he looked as if he could be Asian, Black, or some combination of those two or more.
That Goon wore a beret and had a tattoo on his left cheek. He was not present during the Incident at the Flugelheim. That Goon attacked Batman in an alley, after the car chase through the streets of Gotham City. He appeared after screaming and flipping over a tall fence. He came at Batman while dual wielding twin scimitars against him. He slashed at Batman, who easily deflected the blades with his shielded gauntlets and boots. Batman struck him on the head but it appeared that he was only briefly stunned. When the Goon came at Batman in a screaming frenzy again, Batman kicked him in the head, which caused the Goon to flip back and land on the ground passed out.
The Swordsman appeared in the 1989 Mega Drive/Genesis game Batman, based on the film of the same name. In it, he appeared in the second part of the fourth stage, Gotham City streets. Similar to his appearance in the film, he jumped out and fought Batman in an alley, using acrobatic flips, and his two scimitars, which dealt a great amount of damage to Batman. He still had his beret and sunglasses, however, instead of the standard Joker Goon Jacket, he had on what appeared to be body armor.
The Swordsman Goon also made an appearance in the 1990 Batman adaption for the PC Engine/TurboGrafx-16 in 1990 (identical to his arcade appearance). He was the first boss in the final stage at the Gotham Cathedral, protecting the Joker from Batman. Here, he jumped and did somersaults and tried to kick Batman. He had his scimitars, however, he did not used them in the fight. Upon being defeated, he fell through the ground, and created a hole that was used in defeating Lawrence. In that appearance, he was wearing all black, and also attacked with his two scimitars, which he sometimes threw.
The Swordsman Goon also appeared in the 1990 arcade game also titled Batman after the film. Here, he appeared as an enemy in the third stage, who again jumped out and attacked Batman right before he could reach the Batmobile in an alley in Gotham (his appearance was identical to how he appeared in the PC Engine/Turbografx-16 game). He also reappeared in the fourth and final stage at the Gotham Cathedral. He and the other Joker Goons tried to stop Batman, who looked to take down the Joker. He fought by jumping, flipping, and slashinging with his two scimitars, which he sometimes threw.