Just because everyone and their mother adds a signup flow just to be able to use their web app doesn't mean it has to be done that way. You can add the signup flow after you've already demonstrated the value to the user and when it would provide additional value, like saving things to your account.
An anonymous user on the web is equivalent to some anonymous user downloading your app from the app store.
It's true. And the article's example actually doesn't have a signup. But often demonstrating value to the user will require multiple accesses and you don't want them to lose the data they've already entered. It's probably better to force a signup then potentially lose everything the end user has done in your app.
For a mobile app, you can store data locally or on a server keyed to the user without any potential for loss and without a signup.
An anonymous user on the web is equivalent to some anonymous user downloading your app from the app store.