Hmmm..
the blank screen means that the file dont exist.
You can try typing the commands in on that screen then saving it as ~/.asoundrc.
Not sure if that would work, if it dont you can delete the file later.
Heres what I have in mine.
Your device number might be different, mine is 0. yours may be 1
Ok added the file
.asoundrc to the directory
and see what you see on your image but have changed the card number to 1.
Still no joy the MAME games they don't run and just return back to the list of games.
My SNES games work well with sound.
For anybody else who wants to help figure out the solution to the problem this is my current hardware set up:
Raspberry Pi 2 Model B (Using a power adapter)
RetroPie v4.2
NEC Multisync LCD 1770 NX (Monitor)
USB Powered mini speaker
and Zero Delay USB Arcade controls