A summary of the story is as follows. Please note, this is mostly from memory, so some of the minor details may be wrong.
Crimson Dragon’s protagonist is a nameless male human who other characters refer to as “kid”. His village was infected with Crimsonscale disease, and he was the only survivor. Crimsonscale almost killed him, however eventually he recovered and became stronger because of it, allowing him to become a dragon rider of Icarus Division, Seeker forces tasked with keeping Crimsonscale under control.
The game begins with you being recruited by Icarus Division. You take orders from Sana (protagonist of Side Story). At the end of the tutorial level you fight a White Reaver, and then White Phantom shows up. White Phantom hasn’t been seen for a while and the Icarus Division’s goal becomes to track down White Phantom. Numerous missions follow from this, and it becomes increasingly evident that the Seeker government is hiding facts from the general population. One trader, Cadmus (who is the game’s shopkeeper and also featured in Side Story), is increasingly suspicious, however Sana advises that it would be wise not investigate what the Seeker researchers and government are doing (the less you know, the better).
Sana tells the kid of the legend of ancient ruins of Amara, where the first colonists on Draco once lived. It was believed that the colonists on Draco no longer had contact with Earth.
Eventually you encounter more white reavers. It is revealed that White Phantom was not actually spreading the Crimsonscale disease directly as originally thought, but using the White Reavers to do so. It is at this point, after some White Reavers are captured, that Sana leaves for a while - I believe that this is when Side Story takes place, with her riding one of the White Reavers, however this is not confirmed explicitly.
In any case, eventually you find the entrance to the ruins of Amara, and enter them. This is World 4 of Side Story, “Original Base”. You re-encounter Sana, suggesting that Side Story has just finished (again, not confirmed). Before you return you are taken in for questioning by the Seeker government. The protagonist describes it as more of an interrogation. Eventually you are released for no particular reason and sent back to do more missions for Icarus Division. Sana warns you that you should forgot all about your discovery of Amara.
Cadmus brings you news of a corpse that was found of a human, that mysteriously matches the DNA of a government official who was still alive. Side note: Cadmus was once a dragonrider of Icarus Division, but he started asking too many questions.
Eventually, you investigate a new location which is a dragon graveyard. However, one dragon is not dead - the skeleton awakens and a boss fight occurs. This dragon is said to be a prototype of White Phantom (although I think possibly a dead White Phantom from another cycle - more on this soon). When defeated, Sana tells you they now have the antibodies required to defeat White Phantom. Soon afterwards, White Phantom appears and the final battle commences.
After defeating White Phantom, a portal opens up in Amara. The protagonist becomes aware of a great body of information. It is revealed that the colonists never actually lost contact with Earth; they were lied to by the government. The government had gained the ability to “reset the planet”, and it is implied that at this is done via tampering with the multiverse. Draco is actually a huge laboratory designed by the government seeking immortality (presumably by genetically altering people with Crimsonscale). This cycle is deemed a failure, and the planet is indeed reset once again. The protagonist tells us that “this is the end for us, but also the beginning”. Before the planet is reset, the protagonist leaves behind a recording telling whomever may find it that Amara and White Phantom are the key, and to seek them out. This, he says, will lead you to your freedom.
The end credits roll. In a post credits scene, implied to be in a future cycle, the kid tells Cadmus that a recording they found was stupid - that there is no government conspiracy. However Cadmus is suspicious, so they get on their dragons and ride off into the distance in search of Amara.
To be continued in Crimson Dragon Saga?