The idea of using kangaroos for sport is well documented by artists such as S.T. Gill, Thomas Balcombe, Edward Roper, Eugene von Guerard and Edward Winstanley, and many first hand written accounts also exist. Hunting in the manner of English foxhunts was popular from the early 19th century in Australia. Hunting clubs were established in Australia, often using the same rules and riding habits as in England.

Less well documented is the driving of animals for culling, as depicted here. By the 1870s large scale destruction of animals – including rabbits, dingoes and kangaroos – was not unusual, especially in times of drought, as a means of controlling the population and alleviating damage to agriculture. In 1882 the rounding up and destruction of animals was acknowledged in the NSW Pastures and Stock protection Act. 

The principal method was the kangaroo drive, or battue, derived from the Aboriginal hunting method of beating bushes and woods to flush game into an enclosed space, similar to the scene depicted here. Thousands of animals could be killed using this technique.

Reference:
Kangaroos : biology of the largest marsupials / Terence Dawson. Sydney : UNSW Press, 1995

Signed lower left, possibly Hailey or Bailey?