If the interface layer between a user and a webpage is graphical, then that website has a GUI.

Then anything on a screen is a GUI, as is every website.

Yet, most would consider the term to refer to purpose-build interfaces, rather than those build upon the 'GUI' of a web-browser - which has it's own idiosyncrasies.

If google docs doesn't count as a GUI then i dont know what does.

Every native toolkit has its own idiosyncrasies. Some are closer to the OS official look, which changes along the years, some are different. I'm for a relaxed definition: if it's graphical it's a GUI, if it's text it's a TUI. Then we have larger or smaller rendering libraries. The browser is a particularly large one but often it's got the advantage of automatic app updates.

Is an interface within a web browser not purpose-built? I think of “GUI” in contrast to “CLI” — which, yes, is inclusive of almost everything you interact with on a computer, including websites.