It appears that this is sidewall flashing with shingles installed underneath, but I don’t want to put my foot in my mouth if it’s just another sort of component I’m not aware of… but I don’t feel any sidewall flashing under the shingles either.
This is improper, correct?
If you are still onsite, go gently lift this edge shingle and see what is under.
That’s how we learn. 
The only dumb question is the one you don’t ask. 
When you looked up here, was it step flashing?
If so, they are simply using the uncommon flashing as counter flashing and no issue then.
Poor sidewall siding roof deck clearance.
More FYI detail: If you get the opportunity during an inspection, it’s good to see if the counter flashing you pictured is overlapped by the house wrap/felt paper (weather resisting barrier). Usually that detail is hidden by the siding, but the overlap of the weather resisting barrier over the counter flashing in “shingle fashion” is the correct construction method.
Image: Look at the counter flashing overlapped by the house or building wrap “(WRB)” on the top of this image:
