Burgstaller began his sporting career as a Nordic combined athlete. In 2002, the student at the Stams boarding school for skiers in Saalfelden, Austria, took part in his only World Cup competition. In the sprint of the B World Cup, he finished 54th.
Burgstaller has been active in bobsleigh since 2006. At the start of the 2006/07 season he started first as a brakeman in the team of Juergen Loacker in a competition of the Bob World Cup . At the four-man Bobsleigh World Cup in Park City , the team finished 18th. As the best result of the season, the team achieved eleventh place at the 2007 four-man bobsleigh World Championships in St. Moritz , Switzerland . In the following season, Burgstaller switched to the position of brakeman and also started with Loacker in the two-man bobsleigh for the first time. However, they were only able to place in the top twenty once. In the four-man bobsleigh in St. Moritz, they first made it into the top ten. In the victory of the Latvian Jānis Miņins , the team finished eighth. Burgstaller also started at the Junior World Championships in Igls in 2008 . Together with the pilot Anton Hörhager , he achieved twelfth place in the two-man bobsleigh and 14th place in the four-man bobsleigh. He also competed in the two-man bobsleigh with Hörhager at the 2008 Austrian State Championships. When Jürgen Loacker and Johannes Wipplinger won, the duo won the bronze medal. In the four-man bobsleigh, the state-certified ski jumping instructor started again in the Loacker bobsleigh. They won the silver medal behind pilot Wolfgang Stampfer's bobsleigh . He drove his last major competitions in January 2010.