From the article your "password" is a:
short-lived one-time-use tokens delivered over a secure channel that they control
So, your session times out, log in again by requesting a new one-time-use token delivered over the channel of your choosing.What to log in using a different browser, it's the same as before, get a new token.
You get the idea...
For example, say your session has timed out. You click the log in button and provide your username, and a couple of moments later you receive an email with a one-time-use link that you click to take you back to the site and log you in.
Another example: you click log in and provide your username. A few moments later you receive a text message with a 6-7 character one-time-use token that you type into a text field on the web site. The web site then logs you in.
In both cases the login requires you have immediate access to a secure channel you specified at the time you set up the account. The token or link provided via those channels are only valid for a single use and if left unused expire in a fairly brief period regardless.