The rules of the game are fairly straight-forward, but is it really that much different than a "railroad" RPG module by a RAW-obsessed DM?
As I said, playing by the rules. For example, I can't "hail a taxi" in Arkham Horror instead of moving by spending my move points along the line. I can't gather clues outside of the normal method, I can't make any decisions about my character other than the prescribed actions dictated by the rules of the game (exactly like Monopoly or if you want to use cooperative games, Castle Ravenloft boardgame).
If you can't make fictional choices that impact the outcome of the game, it's not roleplaying.
I can play any game and plaster a "story" over it to describe what happened. That doesn't mean it's roleplaying.
There's a reason why Castle Ravenloft is a boardgame and not an RPG expansion.
Could I hack Monopoly, Arkham Horror, Chess, etc. with rules of my own to make it a roleplaying game? Yeah, sure.
But, I said, as-written. Roleplaying games have a design that is fundamentally different from boardgames. And, that's why the "rules matter".
Again, I didn't say rules = no roleplaying. In fact, I say the opposite. In order to make Chess a roleplaying game, we need to make rules for that. If I want my White Knight to betray the White King, I have to make (or change) a rule for that.
A lot depends on what you want whatever game you play to be and how obsessed you are going to be over rules. While it does go kaput if a boardgame turns in to Calvinball, there's still a lot of room for story even in some of those. The clear delineation between game types is rather blurred, for many reasons. I don't mind wielding the eraser myself when it makes something more fun.
Would it be my first choice for roleplaying? No way in heck, but when the group is right it can morph in to an RPG-type experience.
Story does not = roleplaying.
It's like me playing Stratego and saying, "Oh, this piece is a soldier and back home he has a wife and children. We'll send his belongings home when he's blown up."
We have a story right? Did we roleplay? No.