Sure! Here's a simple game that meets all the requirements specified:
To play the game:
1. Save the above code as an HTML file (e.g., `game.html`).
2. Open the HTML file in a web browser (preferably one that supports touch events, like Safari on a smartphone).
3. Tap on the canvas to move the bag and try to catch the falling emojis.
4. Your score will increase whenever you catch an emoji.
Note: The implemented game uses emoji code points as pictograms. It starts with a score of 0, and the bag moves horizontally to the tapped position on the canvas. The emojis fall from the top of the canvas, and whenever an emoji overlaps with the bag, it gets caught, increasing the score by one. The game continues indefinitely, with emojis falling at regular intervals.