The 13 highest earning Japanese films are all anime. The 25 highest earning Japanese films are all, except 2 of them, anime.
And as for those 2 movies? Well, therein lies a story.
In the mid-90's, Fuji TV funded an 11-episode drama series that aired for 2 months, called Odoru Daisousen (Bayside Showdown). It's a light-hearted police drama with comedy elements. It's good. It was somewhat of a hit.
The director (Katsuyuki Motohiro), most of the cast, and the writer were all pretty new. The amateurish approach made it quirky, but interesting.
Somehow, the decision was made to make a movie. So they did, slightly reinterpreting the ending. It very much drew inspiration from Western police movies which were popular at the time, but kept the non-serious tone of the drama series. It was released around the same time as Rush Hour, so it drew in crowds.
A second movie was made, which is currently the highest earning live action Japanese movie, at #14. It was released in 2003, tackling issues such as mass surveillance and vampires with the same lighthearted tone.
They went on to make 2 more movies, which weren't quite as successful.
As for the director... well, he went on to direct a little-known anime called Psycho-Pass.