The only problem I see with it is that it is wrong

. His list of religions are those that have missionaries now. In the past other religions have had missionaries. If you want to be more accurate all religions go through a period of wanting to spread themselves far and wide. "Rapture" had that mechanic and one that had religions go obsolete, both don't work with the "Choose Religions" option. So if I did something like it I would have to be able to turn some bits off based on game options which currently would require having two sets of religions.
Not quite. Most of the older, "Pagan" religions felt no need to spread the word of their gods to far and distant people. Most of these religions were pretty ethnocentric. Here is a religion by religion breakdown of the religions we have, and the manner by which they spread in the real world.
Shamanism - Shamanistic belief systems are widespread across the world, and have little in common with one another, save for belief in the living spirits of all creatures (and sometimes plants) and of the shaman's power to transcend the physical world into the spirit world. Nothing that could recognizably called missionary work ever seems to have gone on among the Shamans.
Druidic Traditions - Similiar in some ways to Shamanism, with their animistic beliefs and the Druid as the central figure of the religion who can communicate with the spirits, faeries, and Gods alike. There is a marked difference here, however, as the Druids themselves were /very/ secretive about their practices. We know nothing about how the druids practiced their religion, as the Romans systematically destroyed them, and they left no written records behind. What little we know of Celtic religion is from surviving Welsh and Irish works written down by Christian monks. Given the secretive, guarded nature of the religion, I think it is safe to say that missionary work never occured. This was a very ethnocentric religion, practiced solely by the various Celtic peoples.
Tengriism - Another Animistic religion, with Tengrii sitting atop creation as an over-God figure. This religion became fairly widespread due to the far-travelling nature of it's nomadic followers. No missionary work seems to have occured, and the followers of this ancient belief readily abandoned it in favor of Islam and Buddhism.
Ngaiism - This is not a religion I will claim to know much about, but I do know that it is practiced solely by the Maasai people of Kenya and Tanzania. This one seems to be a polytheistic/animistic religion as well. Given that it's adherents never spread the religion to neighboring peoples, I think it is safe to say they never engaged in missionary work.
Shinto - A term for the indigenous beliefs of Japan, this is another animistic/polytheistic religion. There was never an impetus to spread this to outside peoples. Later Japanese Shinto adherents blended the religion with Buddhism, to the point that the two religions in Japan seem to have become one syncretic belief system. Many Japanese view Shinto as more a way of life than a religion, which, although it is not true, does reflect the Japanese attitudes towards Shinto. Shinto, like most of these animistic/polytheistic religions, do not view themselves as existing to the exclusion of other belief systems. They simple are.
Asatru - Although we most readily associate this belief system with the Norse, these were the gods of all Germanic peoples at one point in their history. This religion never seems to have spread outside of the Germanic peoples. It is worth noting that this religion did not have a real name (beyond 'Norse Mythology') until recently, when neopagans brought the ancient beliefs back to life.
Confucianism - Some debate whether this can truly be considered a religion, or a philosophy that has been followed by the Chinese through the centures with a religious zeal. What is without doubt, however, is that Confucianism does not deal with the heavens, the afterlife, spirits, or any other such matters. It is entirely a moral and ethic system for living one's life and governing others. Chinese spirituality is a folk belief system, centered heavily around ancestor worship and the Celestial Bureaucracy. Confucian belief heavily influenced neighboring peoples, but few people would call themselves "Confucian", unless they were students of the philosophy itself. This one is tricky to call, but, I would say that the Missionary unit is applicable here, as teachers who spread the philosophy.
Hinduism - Here we find the first religion that can unequivocally be stated to have engaged in some level of missionary work. In ancient days, Hindu teachers were very active in Southeast Asia, and in the modern day, many gurus have spread their teachings to a receptive western audience (Though there is considerable debate as to whether or not groups like Krishna Consciousness [Hare Krishna] can be considered Hindu)
Jainism - The Jain religion spread very quickly across India, especially during the time of Emperor Samprati, but eventually lost influence to rising Hindu devotional movements. Jain monks do not travel overseas, but beyond this, there does seem to have been some limited level of missionary work. A devoted Jain ruler in Civilization could certainly have chosen to focus on this and make missionary work a priority.
Buddhism - One of the big three (Christianity, Islam, and Buddhism), this one requires little discussion.
Taoism - Without delving into too much discussion about the religion itself, the belief system certainly was spread by teachers like Lao Tzu and Zhuang Zi. The religion does not seem to have spread from China, except alongside Chinese immigrants. Like Confucianism, it's sister-faith, this religion could potentially be considered to have missionaries in the form of teachers.
Zoroastrianism - Zoroastrianism does not allow converts. In recent years this has come under heavy discussion, in no small part because the faith is in danger of dying out entirely. No missionaries.
Judaism - Judaism forbids proselytizing to gentiles. This one is a no-brainer.
Hellenism - This polytheistic religion undoubtedly spread far and wide, but it did so alongside conquering Greeks and Romans, who built shrines and temples to their Gods in foreign lands so that their soldiers and governors would have places to worship. In many cases, local religion was simply co-opted, with local Gods being equated with Zeus/Jupiter, Poseidon/Neptune, etc. No missionaries.
Andeanism - I do not know too much about this religion, for little has been written in regards to it. The Sapa Inca (Emperor) of the Incas seems to have been regarded as a God alongside their pantheon. It appears to have been an ethnocentric religion, like most polytheistic belief systems.
Nagualism - Not only was this an ethno-centric polytheistic belief system, the practice of offering humans as ritual sacrifice to the Gods was considerably off-putting to anyone existing outside the faith. No missionaries.
Yoruba - Yoruba describes the indigenous beliefs of the Yoruba people. Without delving into too much discussion of the religion itself, it appears to be another ethnocentric polytheistic/animistic religion which never spread beyond the Yoruba people, despite the diverse groups of people who came into contact with them.
Christianity - Christianity gave us the word missionary, and has been the most actively proselytizing religion in the world since it's beginning.
Voodoo - Voodoo was originally a West African belief system practiced by the Fon and Ewe people. The belief spread to the west, where it took hold in Louisiana and the Carribean, amongst slaves who practiced it in secret while outwardly pretending to be Christian. Although the secretive nature was undoubtedly because of the persecution they faced, this is clearly not a religion with missionary activity
Islam - No brainer.
Sikhism - Sikhs do, in fact, have missionary groups, and the early Sikh Gurus would certainly be considered missionaries as well as Great Prophets.
Mormonism - Given how many of us have had cheery, smiling Mormons arrive at our doorstep to speak of their religion, the missionary activities of this faith should be obvious.
Baha'i - Baha'is avoid using the word "missionary" and claim to not engage in missionary work. However, the religion does engage in a practice known as Pioneering, where a volunteer of the faith travels to another country to teach people about the Baha'i beliefs. The Baha'is would be quick to point out that the goal is to teach, not to proselytize. However, in game terms, they would certainly be producing missionaries.
Scientology - The missionary activities here should be obvious.