How to make dynamic text in GE? I don't know why, but it doesn't work. I've done everything said in this
video, and my result is the following: planes without a transparent background, only displaying @ as the texture, sitting next to each other. Also, there are a lot more planes than the text.

I have a .blend which can be found here.
Your blend file did not contain the packed font image file, so I replaced the texture with one I googled.
With your plane selected, and switching to edit mode the uv/image editor showed your unwrap as this:
  

For dynamic text to work you need to enclose the @ symbol in your unwrap like this:
  

This change makes your blendfile work as intended for me.