Sure, here's a simple game that meets your requirements:
Instructions:
1. Copy the above code and save it as a HTML file (e.g., game.html).
2. Open the file in a web browser (preferably on a smartphone).
3. Draw on the canvas by tapping/holding and moving your finger on the screen.
4. The puppy is represented by an icon, and a bee will randomly appear on the canvas.
5. If the bee touches the area where the puppy is located, the game is over and an alert message will be shown.
Please note that this is a basic implementation and can be further expanded with additional features and enhancements.