As an AI text-based model, I can provide you with a simple example of how an HTML game can be implemented using JavaScript. Please note that the game's complexity and functionality will be limited due to the constraints specified. Here's the code:
Picture Guessing Game
Click on the correct picture to increase your score!
Score: 0
To use this code, save it as a .html file and open it in a web browser. The game displays four picture icons, and the player needs to click on the correct picture to increase their score. The score is displayed below the images. The game is designed to be played on a smartphone or desktop browser. You can replace the image sources with your own pictograms by providing the appropriate file names.
Please note that this is a simple demonstration, and you can customize and expand the game according to your requirements.