From my local machine (Windows 10) using the command-line, can I fork someone else repository without having to use the Fork button on the site?
Unfortunately, "Forking" is not actually a git function.
By this I mean that without extra plugins or scripts, git by itself does not have a function "fork", nor does it know how to ask the remote how to do a fork.
Instead, this is purely a function that the hosting partner provides, usually through its web user interface.
As such, I think your best way forward would be to either find a script or plugin or program that asks GitHub to do this fork, or build one yourself using this REST API.