I don't know about the rest but this is truly not a complete book. There are no monsters nor even rules for how to make monsters. There are no magic items nor any rules for how to make magic items. AU/AE presumes you have a 3.0 DMG.
I don't have Arcana Unearthed, so perhaps that's what you are referring to. However, my Arcana Evolved has monsters, item creation feats, and a setting primer all in one book.
It was billed as a variant Player's Handbook, so yes, the DMG was recommended. Don't know that I'd call it essential, however, and I could get by without it if I had to do so.