Finished reading it Friday and gave it a couple of days to percolate.
Don't regret purchase and enjoyed it. Not 5 for 5.
First, no it's not written in Lovecraft's style. Most efforts to do that fail horribly in my view so I don't expect or want it, an author has to have their own voice and use it well not mimic another's. The writing style was okay, it didn't sing to me and make me think "I want to find other books written by this author" but it also didn't annoy me and make me "not that name to avoid it future". Of course, my "sing" standard is high and mostly composed of dead people - Dashiell Hammet, Raymond Chandler, Elmore Leondard, Daymon Runyon or Lovecraft sing to me for example.
Second, it is indeed an "Arkham Horror" book and features many characters from the game and works in elements of their "story so far" material in fun ways. As an Arkham Horror the Boardgame fanboy, it was fun to see these trademark characters show up. This alone carried me through 2/3 of the book enjoyably seeing things that I can imagine in the boardgame (of course defeating that monster gains an exotic item) but more Lovecraftian (except of course you don't defeat a monster by shooting it).
Otherwise the "many different characters each experiencing bits of the big picture" approach is one that does work for a horror/mystery story.
As the start of a trilogy it has an arc that ends in this book but that is part of an arc continuing on. So you get "some resolution" but have something big left open.
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I think if at least one "named Arkham Horror" character had died or turned out to be a villain that would have created more suspense going forward. Nobody should be "safe" for a good level of tension. Perhaps the "punch" is being held for book 2.
About 2/3 through I started thinking it was obvious one character was a villain. This wasn't resolved by end of book but remains a possibility. That is actually not all that bad as it draws out the question about them. Hopefully they are somewhere in middle as grey complicates things.