Ah, OK, I see his trick. He is sourcing/sinking current directly with the Arduino and multiplexing the anode sources and cathode sinks in a 2x4 array (for 8 drivers and 8 sinks).
But that's not the circuit you're using 
I'm guessing you're trying to "uber-multiplex" the whole thing by putting his 8x8 array of LED's into greater arrays and just generalizing his solution with top-side NPN transistors but that's not going to work (as you noticed
You will have more luck adding additional NPN transistors at the bottom and switching them between the 8x8 grids.
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The Gadget Shield: accelerometer, RGB LED, IR transmit/receive, light sensor, potentiometers, pushbuttons