I just can't get it to refer to the index itself.

I don't understand the problem.

You saw from the other posting you can use:

int row = table.getSelectedRow();

You load the data into your table you know what column contains the filename of the song you want to play, so you just do:

String filename = table.getValueAt(row, ???);

I know how to play the song

So then you play the song.