Not that we can take the story for this game too seriously, but here's the story from the game and instruction manual. It confirms Christopher's position in the timeline pretty well. It does make it seem like Dracula has been defeated by the Belmont's many times before Christopher though, but perhaps it is talking about Dracula in general in the first few sentences and then takes us to the "now" part when it says "100 years have past since Dracula's demise". I'm glad it shows all sorts of flashbacks to Dracula's Curse in the images, but only shows that game.
Of note is it says that only "now" that Dracula is a demon king. Sounds like he didn't become one until after he was killed by Trevor. Possession of the Crimson Stone and Death at his command wasn't enough before? Guess he needed to take a trip to hell first. They totally need to tell the story of how he became a demon king at any rate.
Also, this is the first time I recall him summoning monsters by using innocent people as sacrifice. Sure, he's sacrificed people to increase his power, which might be the same thing, but maybe this represents a shift of using alchemy and devil forgery to create monsters to summoning them from hell using human sacrifices?
Another tidbit of note is that it doesn't mention Dracula getting revenge on the Belmont Clan like the localized US version of Castlevania: The Adventure or Castlevania: The Belmont Legacy comics. He just rose up for round 2 against humanity and Christopher decided to head out to stop him.
From the game:
Count Dracula, a demon king with a once great demonic power who seeks to hold the people of this land in the grip of terror!
Time after time, throughout history, Dracula was defeated by the Belmonts, a family of vampire hunters who brought peace to this land.
100 years have past since Dracula's demise, and with the fear of him gone, he rose again along with his castle to scourge the land with his evil.
With such a tragic history repeating itself, Christopher, a descendant of the Belmonts, decided to stand up for humanity against the demon. He alone seeks to infiltrate the dark castle where demons run rampant.
From the instruction manual:
This goes way back...before the era of Simon Belmont.
The evil Count Dracula built his castle in the suburbs of Transylvania, summoning monsters from the other world by using innocent people as sacrifice.
Now that Dracula has become a demon king, Christopher Belmont from a long line of vampire hunter ancestry set out on his journey to Dracula's castle in order to defeat him.