You are correct, the standard is called OpenPGP, from the software PGP or “Pretty Good Privacy” by Phil Zimmerman. GPG, or Gnu Privacy Guard, is an implementation of that standard. Arguably, it is the most popular implementation and therefore the most widely known.
When designing UI interactions and writing documentation, we have to consider multiple audiences. Not only do we have to consider a highly technical audience with background and experience that understands these distinctions, but we also have to ensure that the UI and documentation is approachable for less technical or even non-technical people. For the less- and non-technical people, we have to use the term that they are familiar with, even if it is, at times, less correct in the eyes of someone with more knowledge. “GPG” is the term that is used more frequently in the git documentation and, also, it is the name of the feature in git configuration. So if someone is looking at the git documentation and then goes to our help docs looking for information about GPG support, they can find it as it stands currently.
As to your analogy, I think a more apt comparison would be writing something like, “Open your browser and navigate to http://example.com,” instead of “Open your HTTP(S) client, issue a request to http://example.com, and wait for the response to be rendered.” Both are correct. The second is more accurate on a technical level. The first is more likely to be understood by a wide variety of audiences.
I will, however take this feedback to the documentation team and see if there’s some clarification that could be added.
I hope that helps!