Regarding U+2016 and U+2225, it seems there used to be some inconsistency between implementations of different operating systems in the age of Shift-JIS. As Unicode (and JIS X 0213) have been widely accepted, U+2016's mapping to the DOUBLE VERTICAL LINE glyph also has become stable. On the other hand, the DOUBLE VERTICAL LINE glyph itself has long been implemented in most Japanese fonts, since the days when neither JIS X 0213 nor Unicode were widely accepted, with the 'vert' table including its vertical glyph using the －90 degrees rotated shape.
Also, it is known that the DOUBLE VERTICAL LINE glyph is used to represent the norm of a matrix in mathematics.
On the other hand, because JIS X 4051 defines a set of note "reference marks" including the DOUBLE VERTICAL LINE, the JLREQ document seems to regard this character to be one of the note reference marks used in Japanese typography.
However, as far as I suspect, the reason why JIS X 4051 defines this character to be a note reference mark is not very clear. (By the way, this character is usually called 'parallels' in Western typography, according to Robert Bringhurst's book mentioned below).
As Ishii-san mentioned, Wikipedia also has a page introducing the character as a note reference mark:http://en.wikipedia.org/wiki/Footnotes
However, look at the sentence written by Robert Bringhurst quoted in the Wikipedia article. According to Bringhurst's The Elements of Typographic Style,
the following marks: section, parallels, and pilcrow should not be used as note reference marks today, because use of them is obsolete and can confuse the reader.
Similarly, Chicago Manual of Style,
16th Edition, allows all such reference marks to be used for tables, but it says only asterisk, dagger, double dagger, and section should be used for note references in the body text.（p. 666, p. 148）。
Hence, it can be said that the "parallels", viz. the DOUBLE VERTICAL LINE glyph is not used widely for publications today.
In addition, as I mentioned in the beginning, many Japanese fonts have used the －90 degrees rotated shape for the vertical writing mode, with the help of the 'vert' table, and this makes it clear that using the －90 degrees rotated shape for the vertical writing mode is the most practical and reasonable usage of the U+2016 character.
For this reason, I suspect that JLREQ's assumption that the DOUBLE VERTICAL LINE glyph corresponding to U+2016 should be regarded as a note reference mark, is incorrect in practical publishing and printing contexts in Japan.
Also, for the reasons mentioned above, I think the vertical posture of the U+2016 character should not be "Upright", and it should be the －90 degrees rotated shape, as represented by using the 'vert' table in many Japanese fonts available today.
1. Robert Bringhurst, The Elements of Typographic Style, Second Ed., Hartley & Marks, Point Roberts and Vancouver 1996.
2. Chicago Manual of Style, 16th Edition, The University of Chicago Press, Chicago and London 2010.