This game is a good example why you can't always automatically port a game from one platform to another. Having the player-character follow the mouse cursor works well when the user has a mouse, but most Android devices have no mouse, so a different input method needs to be used. In this game, the gameplay is tightly connected to the input method. This means the gameplay will change during the transition from one platform to another.
The most straight-forward input choice would be the touchscreen. Just have the character follow the touch-events, so the user can move their finger on the screen and the character follows. The drawback of this method is that the players finger will cover a part of the screen. In the example game you posted the player only controls horizontal movement. This is good, because it means the player could move their finger along the lower edge of the screen to avoid covering the game action. When they would also control vertical movement, their own finger would certainly get in their way.
A more adventurous method would be to use the gyroscope sensors and have the player control the game by tilting their device. I once played a very similar game on Android which was controlled that way, and it played better than you would expect. However, this input method is less precise than finger or even mouse input, so you might want to make your game easier to combensate.