Similar functionality has been available in Google+ when sharing music; users could listen to or buy music shared from the Play Store. Now, when you share an app on Google+ there will be an "Install" or "Buy" button which will take users directly to the Play Store. This will work on a desktop or on an Android mobile device.
One odd quirk with the functionality is that the new buttons will only be displayed if you share the app link on Google+. If you +1 the app in the Play Store and share it that way, the install option won't be there. It seems likely that will change in the future, but it's an odd omission right now.