Im saying (to me at least).. it looks like you have the CS pin on the SD card connected to two other places on the Atmega
Is that how the other diagrams posted have it? (two places)
I have tried BOTH (with this library)..
using D4 and D10 and the CS pin...
and of course using D9 as the default audio output pin..
this gives you 'basic' audio output.. unless you build in a filter/amp..etc..
(more advanced/better audio output is use D4 as the CS pin.. and use BOTH D9 & D10 for audio output. [along with a few other components])