He started his career with now defunct side ÍK in 1988, but when the club folded due to financial difficulties in 1991 Helgi transferred, with most of the side's players, to the newly created football division of the town's handball side, HK, and played there for a few seasons before moving abroad, becoming one of Iceland's few international footballers that have played in Iceland's lower leagues but never in the top league.
Rúrik signed for Charlton Athletic at the end of August 2005, but failed to make an appearance for Charlton's first team, having played for HK Kópavogur in his youth.
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He also played for RSC Anderlecht, the then champions of Belgium for a year, but did not settle so he returned to HK Kópavogur.