It's a better puppy than *I* can draw.
That ain't saying much, though.
You've got a "NEXT" word button, and the button to take you back is a graphical icon. Make 'em consistent with each other.
The twelve-year-old says, "Lemme do a puppy!" Which counts as a good review, I think, but not a spectacular one.
Might be a nice game...
... but every single one of the levels is locked when I start the game. Unplayable.
I like the idea, please give it more tinsel!
Everybody's saying it, and now I am too: put an easier tutorial in the game. Waiting for the user to his space or something before running the "this absorbs that" video examples would help; I kept going to a tutorial page and immediately some purple thing eats some orange thing before I could even look at what shapes there were.
Naming the criterion for winning explicitly would help too; it's "side A gets a piece that's so big side B has no way of building anything to eat it," isn't it?...
Also, a little sound would be nice. Nothing flashy, but, I dunno, some soft beeps or slidey noises or something when a move is made.
Final boss is too hard
After I go through the tunnels, and collect the thirty-seven Glow Stars, I completely can't get past the giant frog! ... no, wait.
Actually, here are three that would make this game better, without too much effort on your part.
1) Add a timeout after the user guesses wrongly about a symbol. I can spam WASD and get in hits faster than anybody who stops to read the options.
2) A screen with all the hiragana and their Roman equivalents, please?
3) Option to mute the music.
Updated the game! 2 out of 3 of the issues you mentioned have been fixed. Thanks for the input!
Crank-a crank-a crank-a
The animation on the puppy's tail makes it look like a pump handle... a little more deceleration time at the bottom of the wag might help there.
Concept of the week: twitch trading.
Male
Joined on 12/12/10
Cute Puppy - Dress Up 
Demons Took My Daughter 
Shape Chess 
Hiragana Fighters 
Lovely Puppy