Perhaps you noticed in the video that the pattern displayed by the LEDs did not change AS THE SWITCH WAS HELD DOWN.
It changed only when the switch was pressed and released.
Therefore, the first thing you need to do is make things happen, like counting, only when the state of the switch changes. You'll need to record the previous state of the switch at the end of loop(), and read the current state at the beginning of loop(). In between, you determine if the state has changed, and if so, whether it changed to pressed or released.
Once you have the counting working, changing how the Arduino manipulates the LEDs as the count changes, is trivial.