I can only imagine he thought (for some strange reason) that you were only wanting a single matrix of LED's, which would indeed make the extra IC's rather pointless. However, for a number of arrays (as in your case of 29), using the existing logic chips and drivers is the only thing that makes sense.
Using an Arduino should make it fairly easy, it's vastly more powerful than the old 6502 system, and much more capable of the job.
So it's really a question of working out exactly what signals you need to provide for the CD4015's, and then programming the Arduino to provide it.
There's plenty of information about using the Arduino to feed shift registers, and libraries to do so - it shouldn't be too difficult to modify those examples.
https://www.arduino.cc/en/Tutorial/ShiftOut