Good news: The universal Windows 10 version is certified for the Windows Store.
Birthday Hub for Windows 10 does support Continuum and does synchronize the data you added inside the app with all W10 Devices with the same Windows Live Id where the app is installed.
You can also import the data from the W10 version to the WP8.1 version via the OneDrive Backup (only in the full version).
You can install Birthday Hub for Windows 10 on your Windows 10 Mobile Phone, on your Tablet and on your Desktop PC.
It is a free upgrade if you already bought the WP8.1 Version. If you like the app and you would like to support further development by buying the full version you will get it for up to 10 devices, your W10 Tablet, your Windows 10 Mobile Phone and your Desktop PC.
The trial version does have some small limitations but the main features are full functioning.