The web-browser based release of the Twine 2.x application stores your projects within the Local Storage area of your web-browser.
The application has two options you can use to export one or all your projects to another web-browser, either on the same machine or a different one:
1. The Archive option [All projects]
This option creates an archive HTML which contains all the passage data for all your projects.
2. The Publish to File option. [Single project]
This option creates a story HTML file which contains the passage data of a single project
Now you can use the Import From File option to import either the archive HTML or the story HTML into a new instance of Twine 2.x application.
WARNING: Any project changes you make in the either instance of the Twine 2.x application will not be automatically available in the other instance, you will need to repeat export / import process to move those changes between instances of the Twine 2.x application.
NOTE: If you were using two instances of the Desktop release of the Twine 2.x application then you would have another method available to you because that release stores it's projects as files on the local hard drive, and you could simply copy these project files between machines as needed.