Tobby Sling Shot
Toshiba Corp offers a series of Flash games on their Japanese website, and Tobby Sling Shot is one of them. While that may not be a very accurate translation of the name, it does describe well the primary gameplay mechanics. Use the mouse to click and drag the platform Tobby stands on like a sling shot to catapult him into the air. Aim him to catch gems and to reach higher platforms. Make your way up to the top of the level to save your girlfriend, Jelly Tobby from the clutches of Bull Tobby. A charming platform game with unique gameplay mechanics. Click.
The art style and game physics lead me to believe it's another creation by Yoshio Ishii. This game would also translate well to the Nintendo DS touch screen interface.
Update: It seems that Toshiba has taken the Tobby games offline. =(