Sure, here's a basic implementation of the game you described using JavaScript and HTML. You can copy this code into a single HTML file and open it in a web browser to play the game:
The game provides a canvas on which you can move a player (represented by a blue rectangle) using mouse movement. Falling stuff (represented by red rectangles) will appear from the top, and you need to shoot them by clicking on them. Each time you successfully shoot a falling stuff, your score will increase. The game keeps track of the score and displays it on the top left corner of the window.