Google has continued to improve the Android Messages desktop client, most recently with an updated Material Design look. Perhaps in an effort to make it work better with Chromebooks (as part of the 'Better Together' feature), the Messages site is now a Progressive Web App, so it can be installed as a 'native' application.
Android Messages web app installed to Pixel C home screen
Much like the Google Photos PWA, Messages doesn't appear to be taking advantage of any Progressive Web App features, like background notifications and offline support. It does have an app manifest, so Messages can be installed to the app drawer on Android/Chrome OS, or the Start Menu on Windows.
If you want to try this out for yourself on Chrome, just open the Messages web app and select 'Install Android Messages' from the main overflow menu (three dots on the top right).