Is it possible to do in-app purchase via play.google.com using my desktop browser?
As far as I know there is no web-based interface for performing in-app purchases.
In-app purchases are only triggered by the app.
The only chance to purchase an in-app item on your computer would be to use an Android emulator with PlayStore installed (Google provides images with PlayStore) assuming that the app you want to purchase items in is available for x86 devices (the emulator is not an ARM device).
In this case you could set-up the emulator with your Google account, download the app, start the app and purchase what you want from inside the app.