No.
You can't use PWM to dim a matrix unless you synchronise your refresh with the PWM. This can done with chips like the TLC5940 and the multiplex library.
I wouldn't say these are poorly designed. They serve their purpose very well. I can have a LED matrix up and running in minutes and not have to worry about cables, soldering, etc etc. If they can't dim, so be it. If the next version they put out dims, that would be excellent, but for now, I'm very happy with this backpack.
As for the limiting resistors, they do specify you need to feed it 5V.
That is better they have limiting resistors on that one. Still can't dim it though. I think there must be an error in the previous schematic, no matter what voltage you always need something to limit the current in an LED.