Um. Yeah, it's same genre as Monkey Island. Same structure. You said it's an action adventure but there are only about 5-6 fights total in Shenmue, so clearly it has no emphasis on action.
I realize Shenmue is boring. Even I admit this. It's very, very dull. And yet, I still like it despite this. But unlike games that just fall flat and end up being dull, Shenmue 1 is dull...on PURPOSE. Which is very hard to explain and very hard to pinpoint in terms of appeal.
Shenmue II is much better as a game. It features open cities with tons of things to do, three different locales, a multiple chapter spawning martial arts story, intense and crazy moments. It is the ying to Shenmue I's yang. If Shenmue I+II HD ever becomes a thing, I highly suggest picking it up, at least at a cheap price. The amount of people I know who aren't big on the first Shenmue but are unadulterated fanboys of its sequel is too high in number.