My question is essentially the title, can you get a mobile authenticator on a Windows phone?
Also related do you need the app for the mobile authenticator? I can't find any information either way but I think you do.
I have Steam Guard on my Lumia 950XL which has Win 10 Phone OS.
Guard works perfect from here, just annoying Family Protection, but it was my decision.
Recommend to all of you.
P.S, i know question is old, but it is still good to have correct answer. And I'm using Steam on it for year at least, may be more. So it was there around 2016, since May at least.
The instructions for Steam Guard: How to set up a Steam Guard Mobile Authenticator on Steam's own website make it pretty clear that only Android and iOS are supported - there is zero mention of Windows Phone.
In either case, it's part of the Steam Mobile app.