I vaguely recall someone else reporting a similar issue once before. Although, I can't remember the exact details.
My understanding is that it's actually more to do with the way NuGet resolves references than anything else.
Unfortunately, I don't know of any way to fix this issue. The best you can do is work around it by manually referencing the DLL yourself like you mentioned or perhaps compiling MonoGame.Extended yourself and turning it into a library that can be referenced from UWP (I'm pretty sure someone else did this once).
There's nothing that I'm aware of in MonoGame.Extended's actual code that prevents it from being used in UWP. Only the quirks an limitations of the various target frameworks, NuGet packages and the NuGet package manager.
That said, if anyone comes up with a better solution to this I'd love to hear about it.