There is a Robert William born Kensington, London on that date but it is not him. The pension card has the right man, as he is in RIC Gormanston.
1878 Oct 27 born Lancs in RIC Register. But his Pension Card gives 1864, which I suspect is correct. However I cannot get any further as I cannot link him to the Liverpool address in 1911 census
1917 Nov 11 Discharged from the Army
1921 Jan 21 enlisted with RIC no 78097. Cook , motor driver & ex-soldier
1922 Mar 6 Living at 72 Roscommon St, Everton, Liverpool on Pension Card