Forward Karl, brother of Edi Kainberger, was a member of the Austrian football team that won the silver medal at the 1936 Berlin Olympics. The Austrians reached the final, where they played the 1934 World Cup winners Italy but, as all their players were professionals, they were not allowed to play in Berlin.
As in 1928, the final score was 1-1 after 90 minutes. Italy scored quickly in extra-time, and the exhausted Austrians were unable to crack their opponent’s defence in the remaining minutes. Domestically, Kainberger played alongside his brother at Salzburger AK 1914 in the Salzburg League, which was not connected with the Austrian national championships.