Chrome desktop does not default to prompting users to add your progressive about to the home screen. This is a very key difference between chrome for android and chrome for desktop.
It may be important for you as a developer to verify your progressive web application will prompt the user to add the application to the home screen. You may also need to test your custom code to manage that experience.
Fortunately, chrome has a way for you to turn this feature on. To do so requires you to go to the chrome flags page and enable the app banners prompt.
The chrome flags page has many settings that you can turn on or turn off the will enable advanced features and new features that have not been fully tested. This gives you, the developer, the ability to test these out and see how they will affect your applications experience. They also give you advanced access to some of these features so you can write and test code that will work once the features are turned on by default.
While you can search the list to find items, I had little success finding this feature through the search. Currently it is located about halfway down and you need to keep your eye out for the app banners choice and also look for keywords like progressive web apps.
When you find the app banners feature to the right drop-down the options and select enable.
This will also trigger a warning at the bottom of the page that you need to relaunch chrome to enable this new choice. Go ahead and hit the button, chrome will close and within a few seconds reopen right back where it was.
At this point you can then open your progressive web app and if you have a valid web manifest file and the service worker with a fetch event handler you should see the prompt to add your progressive web application to the desktop.