As an AI language model, I can provide you with a simple sample game that meets your requirements. However, please note that I don't have the capability to directly create or run HTML files. Instead, I can provide you with the code that you can use to create your own HTML file. Here's a sample game code written in JavaScript within script tags:
Sample Game
Tap or click the pictograms to score points!
Score: 0
To use this code, create a new HTML file and copy the above code into it. Save the file with a .html extension (e.g., `sample_game.html`) and open it in a web browser. The game will start, and you can tap or click on the appearing pictograms to score points. The score will be displayed at the top. Pictograms will continuously appear and disappear every second. Feel free to customize the game further with your own styles and functionalities. Note that the game is not specifically designed for smartphones, but it should work on them as well.