Honestly, I think you could have the Emperor achieve quasi-divine status, in a sort of mimicry of Akenaten of Egyptian fame, or reminiscent of the Mandate of Heaven concept. It would be a bit peculiar, but it might be as simple as an import of the concept from China.
Lets say we have a No-Mohammed scenario, one that leads to a Roman Sri Lanka, Socotra, and Yemen - essentially an arm of the Empire that like in AoM stretches eastwards. (I'm a fan of an oddly naval arm of the Empire, in contrast to the Empire proper).
Historically there are comparisons of China to the Romans (Daqin - Great China) but having the Chinese and Daqin/Fulin interact by sea would be a major moment for world history in that timeline. Assuming some sort of continuous interaction (perhaps a 'String of Pearls' approach, including the aforementioned territories alongside OTL Singapore, and an embassy in Taiwan/Hong Kong/Macau/Beijing) there could be massive transfers of information both ways. The Romans can provide knowledge of the West, and if the Chinese and Romans recognise each other as equals, you could even go so far as to have mutually recognised 'tributary territories'. Who knows. Its China and Rome in contact.
One of these concepts, essentially the Mandate of Heaven resting on the resting Roman Empire could be imported, perhaps even by accident attributed to the Roman Emperor by the Chinese in writing/address, and then included in the Imperial Titles.