You say "a lot of the screenshots and character/creature designs", but you really mean the deer don't you? Yes, we've gotten a few comments comparing him to Yakul, Ashi taka's friend and faithful steed from the movie in question.
All I can say in response is that we're flattered by being compared to Hayao Miyazaki, one of the greatest creative minds in this century, but certainly we can't be accused of borrowing from him any more than we could be accused of borrowing from Lawrence of Arabia if we used horses instead. In fact, my first encounter with a character riding a deer instead of a horse was in a Frank Frazetta painting entitled Tarzan and the Ant Men painted in 1972. I was also quite influenced by an Author named Clara May Allen who wrote a book called "the valley of the caribou pipers" in which children rode on the back of caribou.
While Hayao Miyazaki gave you Yakul to delight in watching, we give you something that you can actually ride for yourself. As wonderful as passively enjoying Yakul was, I think trying to compare an interactive version to it is like comparing apples and oranges. Both are great, but they're very different things fundamentally speaking.