I really liked the game a lot, very nice job on it!
I liked being able to transform between samurai and kitsune and the different movement and attack, very nice on that!
A few things I noticed which may help to improve it:
First, I think that the dialogue is fine in the center in the rest of the game.
However in the very beginning, two different people are talking, I believe, right?
It might be better if only in the beginning of the game, the dialogue box was moved towards the left when one speaker is talking, and moved towards the right when the other is talking.
That way it may be easier and quicker for the player to tell who is speaking in the beginning of the game.
Next, I think it should be possible to skip the intro with a button, or holding down a button long enough if you really want to be sure the player isn't accidentally skipping it.
Even if you are loading the browser for first time, what if you played it before and wanted to play it again later from the beginning again?
(or, perhaps, may need to start over because there was a bug in the game?)
By the way, I got the following bug once while dying as well in case it may help you:
(a very short video of the bug I got, should be shown below that you could play. If it's not showing, please reply and let me know. Thanks)