MAX7219 can be used with the parts you bought.
You need to change wiring.
For example, pin 13 of your BS part is connected to the pin on the MAX7219 that would normally be connected to pin 5 of the AS part.
BS AS
== ==
13 --- 5
3 --- 2
4 --- 7
10 --- 1
6 --- 12
11 --- 8
15 --- 14
16 --- 9
9 --- 13
14 --- 3
8 --- 4
12 --- 10
1 --- 6
7 --- 11
2 --- 15
5 --- 16
I had to do this myself.
Once you do that you don't have to change the code.