Hi @withaplomb ,
Researching your problem further reveals that not all Android OS devices can play .wma files with their stock music player. It varies depending on what types of media file support the manufacturer has decided to incorporate into the OS. Your sister's tablet appears to be one of them. I cannot find out what video / audio file types it does support. Information on this tablet is limited
The workaround is to install a 3rd party media player app which does support the format.
Here is one that you may wish to consider. I have no experience with it in an Android device. I do use VLC (Windows version) in my Win 10 PC as it supports some video files that Windows doesn't and find it very good and it is free. You may already know of a different good Android OS media player and wish to use that. Just ensure that it is compatible with the Android OS version in the tablet and that it also supports .wma files and / or whatever other type of files that you wish to download and play.
Alternatively if you have the time and inclination. you could convert the .wma files to .mp3 files and then transfer them to the tablet. Just search online for convert .wma to .mp3 to find results.
Hopefully this is of some help.