Zinaja was born in Budapest (at the time Austria-Hungary). He was member of the Kingdom of Serbs, Croats and Slovenes team at the inaugural 1924 Winter Olympics in Chamonix where he took part in both cross-country skiing events.
Zinaja spent his entire career with HAŠK (Croatian Academic & Sports Club). As member of the Kingdom of Serbs, Croats and Slovenes national football team, he has played only once, on 10 June 1923 in Bucharest against Romania.
Zinaja became first player in Yugoslav football history to be appointed a national team coach.
He led national team as coach from 28 September 1924 to 4 November 1925, during which time team of the Kingdom of Serbs, Croats and Slovenes played three matches.