To me, Haven is the cheapest hill ticket that the producers of the show could actually afford to the Stephen King universe. Just because their ticket only grants them access to The Colorado Kid, they haven't let that stop them from enjoying the larger King-verse from their little corner in the cheap seats.
I love all of the little Easter eggs to King's other stuff -- Shawshank, Misery, the Dark Tower mythology -- because that's what the author does himself, sprinkling in references to other places and people from his various works into his short stories and novels. Haven is definitely a loose adaptation of the original novel but it is also the most "Stephen King" entrenched of any adaptation I've ever seen of his work and I think that alone deserves a small bit of praise.
How do "easter eggs" of Shawshank and Misery entrench this series more in King's work than the actual movie adaptaions of those books? Or how does a loose tv adaption feel more entrenched than things King himself wrote specifically for tv, like Storm of the Century?
Because by referencing the other stories -- and in the case of the Dark Tower, its symbols and larger mythology -- Haven suggests a larger world than what we see on the show. Shawshank prison exists, the Misery novel series exists, thinnies exist. A majority of the time, King litters his novels and shorter works with allusions to the multiverse of the Dark Tower or call-backs to Castlerock or Derry and the events therein.
What King does in his prose, his quasi-continuity, is what Haven's producers are attempting to tap into with their Easter eggs and, to my knowledge, no other King adaptation -- be it TV series, mini-series, or theatrical release -- has ever really attempted to capture with such a far-reaching net. How Haven is more entrenched in the world(s) of Stephen King than the films you mentioned is the way Haven fully embraces the King mythos while other adaptations limited themselves to just the story at hand.
As for
Storm of the Century, since King himself wrote this and not based on an earlier work, this mini-series cannot be applied to my earlier statement that "[Haven] is also the most "Stephen King" entrenched of any adaptation I've ever seen of his work" since it isn't an adaptation.