How to remove SVG background when the background colour is a mask

This is hard to explain, but I’ll do it as best as I can. I have this vector graphic:
How to remove SVG background when the background colour is a mask
It has a white background that I am seeking to remove. However it seems there is actually no white background. The background is black with a white mask over it, producing the shape below. How can I invert(?) the mask so that it is a shape instead of a mask, and that I can have a transparent background with a black shape? Any help greatly appreciated. The file is here if it is of any help. Thanks in advance!

How to remove background behind a subject (make it transparent), but with a slight transparency blur around the edge instead of sharp cut-off?

I’ve looked at a dozen tutorials on removing background in Photoshop, and they all seem to do the same thing. I’ve followed the usual route of “create a new layer – select your subject – invert selection – press Delete” as described, for example, here. In itself, it does what it should no problem. However, the sharp cut-off from 0 % transparency (the subject) to 100% transparency (background) creates a pixelated edge, extremely visible when placing a dark subject on solid background.

Replacing whiteness with transparency in Photoshop

I want to replace the whiteness in pixels with transparency in the same way as described in this question – i.e. for lighter pixels to be made proportionally as transparent. All solutions found via google are based on magic wand or other methods that do not work for my needs. I’m sure there used to be a way to do this in earlier version of Photoshop (a simple functions to replace a colour with transparency), but I can’t seem to do it in CS6. Replace Colour has no alpha options..