Actually, his math does count replacements. He summed the number of passports issued per year over the course of 10 years because most passports issued are good for 10 years. That method isn't as exact as trusting the government's figure for the number of currently valid passports, but it's a reasonable estimate.

By the way, the government's own numbers on that page don't make sense. They do state that the total number of valid passports in 1989 was 7,261,711. But they also state that the number issued in 1988-1989 was 7,751,633. It doesn't compute that in just two years they issued almost half a million more passports than were valid.