With the complete redesign featuring the new streaming mixin (which I don't use), it seems that when listening to music from my library (stored on my device) I can only shuffle songs within a single album for an artist.
This is not a dupe of this question, in that I'm not asking how to shuffle all songs in the library.
Best Answer
Instead of selecting the artist to display the albums and songs of the artist, tap the image of the artist and the artists songs will play shuffled.