This change means that people who do not use Google Play or other sources, fully controlled by Google, will no longer be able to install applications on Android.
Much of the ecosystem of Android apps that are only distributed outside the Play store will be affected by this, as many developers won't be able or willing to submit to this process or waive their privacy (especially young developers or those making apps that are legal but often targeted by litigious companies, e.g. emulators, YouTube clients/downloaders, BitTorrent clients, etc.)
"After this change you will have to tell Google your real name and home address to install anything on your Android device."
As far as I can tell (and nobody who has replied has contradicted me so far), that isn't true. I won't have to tell Google my real name and home address to sideload [the now smaller selection of] apps.