I was not able to find an exact solution for the question as well (pop up the contextual menu from the keyboard ignoring the mouse pointer position) as it seems that this very contextual menu only pops out from a real mouse right-click and thus all solutions above involve simulating a right-click, hence only making the contextual menu pop from the pointer anyway.
However, one intermediary solution would be to access the whole app Menu Bar (the menu at the very top of the screen right next to Apple's logo) and navigate the menu with the keyboard only. Of course, as its name suggests, it is not a contextual menu anymore, but will eventually give access to the same actions.
To achieve this, the default shortcut is Cmd+F2. (Note: you can change/find the proper shortcut in System Settings > Keyboard > Keyboard Shortcuts then in the Keyboard section, you should have something like Move focus to the menu bar with the corresponding shortcut listed.
This shortcut (Cmd+F2) will let you focus on the main menu so that you can navigate it using keyboard arrows and select any action using Enter or Space directly.
For example, if I am in Finder, I can focus a file with my mouse as usual and then press Cmd+F2. This will highlight/focus the Apple Logo at the very top left of the entire screen (you will see the top left logo highlighted), then I press the ↓, which will list Apple's menu, then I can just press the → to go the Finder menu, then the → again to see the File menu, etc... then with ↓ and ↑, I can go to the specific option/action I want, then I can press the Enter or Space to select the action I want. If I don't need/find anything I want, I can either press Esc or Cmd+F2 again to just cancel the whole highlighting.