Sure, here's a simple 2D game using JavaScript that can be played as a finished game on a smartphone. The game stars the main playable character, Peppino, trying to kill the enemy, PizzaFace. Since you mentioned using pictograms, we'll use ASCII art to represent the characters. Copy the code below and save it as a single HTML file:
When you open the HTML file in a web browser (preferably on a smartphone for a better experience), you'll see Peppino as a green rectangle at the left side of the screen and PizzaFace as a red rectangle at the right side. You can control Peppino's movement by swiping up or down on the screen. To attack, tap anywhere on the screen.
Note: This is a basic structure of the game and does not include any complex game mechanics or win/lose conditions. Feel free to modify and expand upon it as per your requirements.