Your man was discharged from the army under King's Regulations, 392.XVI. This covers medically un-fit soldiers. The discharge date appears to be 12 June 1916.
There is an application for a Silver War Badge for a William Hoare of the Manchester Regiment, 8th Battalion whose details appear slightly different. The regimental number is 527. Other details are also slightly different. This shows the man's age as 43. Does this tally with your grandfather's age ? He joined the army on 26 May 1908. This badge was for men who had been in the military but were forced out through illness or wounds.
It is not clear to me if this really is two different people. The coincidence of name, regiment, and similar discharge dates would be remarkable, but not impossible.
If he was discharged in 1916, then he re-joined, presumably after re-gaining his health. If he was 43 in 1916, he would be 48 in 1921.