Yinga Garten has registered their disagreement about the genres applied to this game
Platformer should be added. Most of the time you spend in this game revolves around traversing the environment by jumping up furniture and along the rafters to solve puzzles, collect key items and in general to progress the story. The store page also refers to this game as an 'action-platformer' which I'd personally agree with.
There also seems to be a tower defense element to this game to in the form of optional survival maps which there are tower collectables for. However as this is relatively hidden away and unrelated to any achievements I don't feel its worth adding that genre.