Is this a Hermetic Secret, or do other traditions have the ability? Is the Gift Necessary or could Magic Theory and/or a supernatural virtue/being a being from the Magic Realm substitue?
Bob
You need to be a magus, hence Gifted, to extract Vim vis from a magical aura as described on ArM5 p.94. A Folk Witch (HMRE p.33ff), however, need not be Gifted to work in her witch's kitchen (p.34), and can there extract Vim vis from an aura as well (p.39), fix arcane connections, and do a lot of other lab work.
In case some player tries to bring a coven of un-Gifted witch grogs into a covenant in order to extract lots of Vim vis from its aura, the storyguide might recall the aura variation rules from RoP:M p.10ff. 
Cheers
Open Arts and Magic Theory are needed if you are talking on Hermetics terms.
About other Magical traditions, those Tradition is differents: some has no clue about, and more.... they didn't need it. Others need secrets that are not widespread or commons, but presents. And some has the same need and process.
To me, it's necessary bieng Gifted and has Open Arts, or of course some proccesss to do that.
You need to be able to generate a lab total. Meaning Gifted, Arts opened and thefore have a Magic Theory score of 0 or better (as opposed to not having it at all). For Hermetics.
In more general terms: It seems to be a matter of whether this skill is included in the Magic Theory ability (i9f any) of the tradition. Or else otherwise defined as being part of what they can do, meaning listed as a lab activity.
Are you asking. Can any faerie, demon, magic whatnot do it? Or any hedge wizard? No, not as I read RAW, I believe it needs to be specifically stated. Though they might have specific powers to produce or precure vis.
It was more the social aspect.
If Hermetic Magic is the only way to distill Vis that would be another goodie to dangle in front of people following other traditions in addition to Parma Magica.
See I think I may disagree. I thought there were a number of non-Hermetic traditions that knew how to brew Vis.
Witches, alchemists, and Solomonic magics... though I don't have my books to be sure of the latter. There was another one like the Learned Magician or something I thought that could do Vis extracting as well, right? Ughh... I have made a mess of my post, sorry.
Elementalist from Hedge Magic can distill vis of their element. So a Fire Elementalist can distill Ignum vis.
Other traditions, which need vis for their effects, generally have some way of getting vis.
Exactly how each tradition goes about doing this differs from tradition to tradition. Some just have to find naturally occuring vis (either lying around or inside magic critters), others may have ways of creating/extracting/refining it from auras, others may have other methods. Even those hedge traditions that "distill" vis are probably in-character not doing quite the same thing as magi do, even if the game mechanics are similar (i.e. at the end of the season you have some vis).
I think that generally, the game mechanics work out such that Hernetic magi are typically better than others at extracting vis. But that might not always be true.
You are best to look at the descriptions of specific traditions. At a minimum you should need to be trained appropriately by a vis extracting tradition (and so need to meet the requirements to be a member of that tradition, which might include having your Gift opened by the tradition). If you are devising your own tradition, it's up to you.
Hedge witches can distill vis as well, and change its recipient like hermetics. So no, this is not exclusive to the OoH. I would say that personal armor (parma), safe haven (aegis) and the superior strength of the Hermetic Arts and oganization that will grant that you are not hunted down on a regular basis is what is appealing.