Have you played the first DMC? If you have, the answer should be clear to you.
Sparda was a full demon, so he didn't age like a normal human. Sparda sealed some of his demonic powers (the Force Edge) within the gate and continued to preserve harmony on earth. He fought the armies of hell to keep them from invading the human world. At some point he found Eva, and decided to live the rest of his days as a normal human with her, meaning that he gave up his powers. They had children and Sparda died before Dante and Vergil were born. It is not clear if he died of old age or by fighting demons, but nevertheless, he was alive not too long ago before the twins were born.
Before the Sky cries White Tears of Snow...