The game is called Daruma Otoshien.wikipedia (だるま落としja.wikipedia)
Let me quote Japanese Wikipedia, since the text on English Wikipedia might be inaccurate at the time of writing of this post.
弾丸の先端に形状が似ただるまの下に、薄い円柱を数段重ね、それを横から1段ずつ木槌で叩いて抜き、倒れないようにうまく一番上のだるまを落とすという玩具・遊びである。胴を素早くたたくのがコツである。
Rough translation (I'd appreciate it if someone can edit it with a better translation):
(Skipped text) Under the daruma head are several thin cylinder pieces stacked on top of each other. The game involves hitting the thin cylinder pieces from the side with a mallet one by one, bringing down the daruma head without the rest toppling over. The trick is to hit the body quickly.
Image retrieved from Wikipedia at File:Darumaotoshi.JPG