He represented the Swedish national team in seven Chess Olympiads from 1982 to 2000 and was honored with a silver medal in 1986. Also, he participated in European Team Chess Championships and represented Sweden twice in World Team Chess Championships contributing to the team's victory in 1993. Schüssler won the Swedish Chess Championship in 1990 and managed to score 6/9 in the 1991 Reggio Emilia chess tournament.
Among his other notable achievements, he won the Wijk aan Zee chess tournament (Category B) in 1988, including several Chess Tournaments around the world.
Today, he also engages in chess coaching, contributing further to the sport.