I usually see integral bridges machined to accept an insert that has the dovetailing for the front pivotmount ring. this insert is then screwed in fore & aft.
However on the integral bridge below it seems the dovetailing has been done directly into the integral bridge. Is that the case or am I missing something in the image??
I am just wondering how they get a cutter in there considering the radius of the hole compared to its flats.
You may have to save the image and zoom in for a better view.

The receiver is likely investment cast with the recess cast in. At that point it's easy to mill the internal slot with a single point tool held in a boring head.

Several other ways to do it.... but that would seem to be the easiest.

Here's a good photo of one pivot mount:



I don't exactly understand your question, but in general the front squarebridge is milled to accept a dovetail or insert that acts as the bearing surface for the foot of the scope ring. The depth of the milled recepticle is usually no deeper than the height of the insert.

The inserts are used so they can take the brunt of the wear-and-tear and can be replaced if the mounts ever begin to loosen from use.

Hopefully an expert machinist who's done this before can chime in with the particulars. There are a few different systems in use.