I quite enjoy Total War: Attila, mainly because it allows me to fulfil Late Antique fantasies such as Gaelic conquests of Europe, or restoring the Eastern Roman Empire...

But to your question. In the context of the game, the starting date is 395 AD, the death of Theodosius, which leads to the final split between Eastern and Western halves of the Roman empire under his two sons, Arcadius and Honorius. Theodosius is the one responsible for proclaiming Christianity the state religion of the Empire, and at the start of this period it is very much, as far as the Christians themselves saw it, "One Church", though there is a clear linguistic divide between Latin-speaking and Greek-speaking halves of the empire, and it's also clear that Latin-speaking Christians and theologians are not always up-to-speed on what's going on in the Greek-speaking sphere. Throughout the course of the 5th century, the power of Rome as a see continues to emerge and be formulated in terms of what will later become the Roman Papacy and Catholicism, but it's still relatively nascent. The game-makers' decision to depict it as 2 separate religions makes sense in game-play terms, in that through the 5th century you can already see diversity and different trajectories taking place, while the two churches remain 'officially' united.