Open your GitHub notifications using shift + g, or this button in mail view:

or

The following is very much experimental, and requires

1. Gmail shortcut mode enabled
2. An organization named label as the first label for an email.

Open a selected GitHub notification email thread using ctrl + return(enter) in a list view where the label is present, and/or from any email view.

Install the extension via Chrome webstore

1. Go to Releases and download the latest version.
2. Unzip the folder wherever you'd like.
3. Go to Chrome extensions page (chrome://extensions/) and load the folder as an Unpacked extension.

Just in case if you're not familiar with how Chrome extension is built, you can find all the relevent code in src/inject/inject.js.