Yeah, the only thing I see going for this at the moment is that people besides the hat-wearing Link wear green clothes. Link himself wears a hat - so I don't think this game will really have anything to do with the HoM story.
What confuses me is that the backstory talks about "in the beginning" - so are they saying the Demon King's rise took place a long time ago, before the flood? If so, and there were continent-grade lands on the Great Sea the entire time, why didn't the people of Hyrule just flee there to begin with?
However, I expect this will be cleared up somewhat in the game. Honestly, if every source wasn't telling us this was after
TWW, I wouldn't believe it based on the way the backstory is framed.