Sure! Here's a simple text-based game called "The Adventures of Noggin the Rock" that you can play in a web browser on your smartphone:
To play the game, you can copy and paste the above code into a new HTML file and open it in a web browser on your smartphone. The game will prompt you for your name, and then you can enter different commands to explore the room, open the door, or quit the game. The objective is to find the key and use it to open the door.
Note: Since you mentioned using pictograms, this simple text-based game doesn't include any visual elements. However, you can enhance the game by adding CSS styles or replacing the alerts with custom-designed dialogs and images.