For a long time, I have been influenced and inspired by the work of this great man. A storyteller, artist, and I dare say, Visionary, Mr. Miyazaki has created worlds and characters both enchanting, haunting, and amazing. No matter what your taste or style you will likely find at least one movie of his that you can really like.
I've always wanted to try to work up a gaming campaign based not so much on his work, but his style. His stories often combine whimsical fantasy with very serious overtones. Themes such as war and it's consequences, environmental devastation, growth, self-awareness and discovery color his films in ways that very much appeal to me. These would all make for a good campaign, but it is also his visual style that makes Miyazaki's work so outstanding. This is also the hardest thing to convey in an RPG setting as it requires describing everything in detail to make sure that his style is coming through and this isn't just another fantasy RPG or steampunk RPG.
I also think that his visual style would translate well to a miniatures driven game. Whether that is a full-on war game or one of the hybrid miniatures adventures games, this might actually be a better fit for gaming Miyazaki style. In miniatures the visual style would be more immediately apparent. The stories would be less involved and would constitute more objective based play than an RPG might, but it would still have enough there to allow for some entertaining gaming that went beyond "kill 'em all".