He first came to the fore as a senior staff officer in the British Army in France in the early days of the Great War. As a Lieutenant-Colonel in 1916 he underwent what was for him a highly unwelcome transformation into a senior staff officer in the Royal Flying Corps. This was the result of an urgent plea by Brigadier-General Trenchard to Sir Douglas Haig for a first-rate staff officer to sort things out at the newly established headquarters of the Royal Flying Corps. This Game did so successfully that he remained Trenchard’s right hand man, not only during the war but through all post-war battles to preserve abd then to develop the Royal Air Force. Game eventually retired from the Air Force as Air Vice-Marshal, after which he was appointed Governor of New South Wales. He arrived in Sydney with his family in May 1930. He soon found himself in the midst of a bitter political controversy. He eventually felt compelled to dismiss the Australian Stae Premier, J.T. Lang in 1932. 

Game left Australia in January 1935 to succeed his former colleague and First Marshal of the R.A.F., Lord Trenchard, as Commissioner of the London Metropolitan Police.

One of his earliest tasks as Commissioner was the organisation of the crowd control measures for the funeral of King George V.  This must have brought back memories as he had been the officer in charge of the gun carriage, which had borne the coffin of Queen Victoria at her funeral in 1901. 

He was also responsible for crowd control during the Battle of  Cable Street in 1936, when communist and fascists came to blows on the streets of the East End of London

Game retired as Commissioner in 1945. He died on 4 February 1961.