As an AI text-based model, I can assist you in providing the code for an HTML-based game that involves drawing and utilizes JavaScript. However, please note that due to the limitations of a text-based format, I cannot generate the actual drawing or provide the pictograms directly. I can help you with the logic and structure of the code. Here's a simple example of an HTML game using JavaScript:
This simple game creates a canvas element where you can draw lines by clicking and dragging the mouse or touching and moving your finger on a touchscreen device. The drawn lines are black with a line width of 2. You can enhance this code further to add game functionality or integrate pictograms as per your requirements.