Sure, here's an example of a simple game that meets your requirements. It's a number counting game where the numbers increase in speed each time a new number appears. The game is designed for smartphone operation and uses pictograms.
In the above code, a number is displayed using a pictogram image and is incremented by one in each iteration of the `updateNumber()` function. The speed is initially set to 1000 milliseconds (1 second) and it decreases by 10% each time a new number appears. This creates a gradually increasing speed effect. The `setTimeout()` method is used to schedule the next update of the number after the specified delay (speed).
Please note that you'll need to replace `emozi_himawari.png` with an actual pictogram image file for the number icon. Also, you can modify the styling and design as per your preference.