Getting the death certificate would be sensible as although described as a soldier of the great war he may not have died from injuries sustained while fighting, he may have been on leave and died from illness contracted at home, i.e. flu, or as the result of an accident here.
It is also possible that the CWGC have missed him or not been informed of his death, i.e. he may have been discharged on medical grounds and died some time later, his relatives not thinking to inform his former regiment/war office.
It might also be worth looking for his service record if it still exists and wasn't one of those destroyed in the last war. If you can find it and it lists his regiment you might find reference to him being wounded in the regiment's diaries.