Pitch can be calculated in any unit of measure. You can have 12 lengths of your nose horizontally, and 6 lengths of your nose vertically, and the angle will be the same as if you drew it in inches. Architectural drawings are scale drawings and what scale they are drawn in differs from drawing to drawing. Usually the roof pitch appears as a simple triangular diagram off to the side of the drawing like this:
On the curved part of the tool, you are not PRODUCING the angle, but you are READING it, just like you would read it off a screen, just like you would if it was a digital read out. It's quite an ingenious and deceptively simple little device.
I was a drafter for 18 years and taught vocational drafting school for 9 of them. I think Syl got it right. The way to find out for sure would be to draw out roof pitch triangles to scale at 1/12, 2/12, 3/12 etc. roof pitch, and see if when you set the device to READ OUT 1, 2, 3 along the curve, if the straight edges match the roof pitch diagrams. If they do, that's got to be it. I'm putting my money on Syl this time.