I suppose I would call Umineko a mystery drama with ambiguous amounts of fantasy in the mix. For the first six episodes or so, I’d say the story is mostly an unorthodox mystery told through several orthodox (well, by comparison, at least) mysteries. There’s enough character focused drama in there to warrant calling it a drama as well, but for the most part, all the character building serves the mystery - everything fits neatly into place in the bigger picture of the mystery of what is going on, why, and how.
The last episodes mix things up a bit, though. Especially episode 8 seems to focus on themes related to the mystery - whether some truths should be left undiscovered, gossiping over the tragedies of others, moving on - but not the mystery itself. The series as a whole also carries some strong themes, such as how perspective makes a world of difference, the exploration of which makes Umineko more than just a mystery to be solved. However, as the journey of the reader is largely a journey to understand, the series has its feet firmly planted in mystery as well.
So, the best I can come up with is “mystery drama”, though “drama” is such a nonspecific term that it can be used to describe most anything. It could also be specified that it is a postmodern mystery drama, but I’m not sure if I’d call postmodern a genre.