It installs new version from the Internet, then on reboot it installs the old version from the system partition. Then again. And again. Then you find /data/app/com.google.android.gms-1, ...gms-2, ...gms-3 and so on folders.
I've downgraded successfully. PM me if you need help. You need MiPhone and a special original firmware image for Fastboot, from en.miui.com. After this you may install xiaomi.eu international image again.
But also you do need 7.2, because 7.3 4.4 is broken too.
All works. Deleted /system/priv-app/PrebuiltGmsCore from the firmware then installed com.google.android.gms_v9.0.83-(240-121911109)-9083240_Android-5.0.apk manually.
It seems like Google Play Services are reinstalled on each reboot from /system/priv-app/PrebuiltGmsCore, no matter if it is older than already installed version.
No, it has not fixed the issue. It fixes it only until reboot.
And if you have "problems" having push notifications, then you have no sync. Just go to Accounts - Google - then try to sync. You'll fail.
I tried to embed...
After the reboot no sync is possible until I install the modern version of Google Play Services manually. On the next reboot it rollbacks to Google Play services 8.4.89 (2428711-036), and no sync is possible.
Each time I install it a new folder appears: /data/app/com.google.android-gms1, -gms2...
The problem was introduced in the latest firmware, 7.0.8.0. The same situation is on the Redmi Note 2. The problem is gone after upgrading to 7.1, so just wait for the firmware released today or tomorrow and upgrade.
This problem cannot be solved on your firmware by checking any checkbox...