Oh weird - I definitely intended for there to be save functionality at the rest points. I will take a look and see if I can get that fixed - thanks for the feedback!
It might be that the Rest Points aren't well advertised (you have to walk onto them and interact to discover what they are), and the Save option still appears in the Menu, but greyed out.
Perhaps the Necromancer could tell you to keep an eye out for Rest Points, at the end of the Tutorial? Not sure how hard removing the "Save" option from the menu completely would be, either.