We are working on native integration, but until then you have two options to convert a Google Doc...
The Readable Web extension converts HTML into Readable English. Because Google Doc is an application, it cannot convert the content in a Google Doc unless you first convert it to an HTML document. There are two ways to do this.
Option 1: Share document via "Publish to web" and convert the result
If you wish to make the document available for others, either publicly or within your Google Workplace organization, you can publish your document to the web. If you do not have a Google Workplace organization but you would like your content to remain private, please skip to Option 2 below.
From the File Menu, click "Share"→"Publish to web".
Note the "Published content & setting" section where sharing can be restricted to within your organization as well as. Open up the provided link, which will contain a normal html web page of your google doc content. You will now be able to convert this document.
Option 2: Download your document as a web page and then convert the file.
If you do not wish to publish your document to the web for others to view, you can download the document as a Web Page via the File Menu and clicking "Download"→"Web Page (.html, zipped)". Once the .zip file is download you will need to unzip it and then double click on the .html file, which will open the file in your web browser. Now you can use the Readable Web extension to convert the text.