He played as a hooker and is considered one of the nation's finest footballers of the 20th century.

Alongside Herb Steinohrt, Tom Gorman and Duncan Thompson Dempsey was in the Toowoomba sides which beat all comers including Sydney premiers Souths, Brisbane, Ipswich and visiting representative sides including New South Wales, Victoria, Great Britain and New Zealand.

In the famous "Battle of Brisbane" Test of 1932, Dempsey was forced off the field with a broken arm early in the second half.

Dempsey, his arm placed in splints, began weeping on the touchline because both the ambulanceman and the team's manager, Harry Sunderland wouldn't let him back into the game.

[4][5]In 2008, rugby league in Australia's centenary year, Dempsey was named at hooker in the Toowoomba and South West Team of the Century.