Let me provide an alternative answer that accords with the treatment in CGEL.
In the sentence,
 Despite there being a blizzard in the area, business remained open as usual.
 despite there being a blizzard in the area
is called an adjunct of concession (CGEL, pp. 734–736).
Concessive adjuncts have the form of PPs, mainly headed by the items in [6i], or adverbs, as in [6ii]:
 i although though despite in spite notwithstanding albeit
ii nevertheless nonetheless still yet
In particular, we have the following:
Despite, in spite, notwithstanding, for, albeit
 i [In spite of/Despite the recession,] travel agents seem to be doing well.
ii [In spite of/Despite having grown up in Paris,] Sonia doesn't speak French.
iii [Notwithstanding Ed's reservations,] the agreement is the best I could hope for.
iv [For all our good intentions,] the meeting soon broke up in acrimony.
v The book covers the whole field, [albeit somewhat superficially].
Despite takes an NP complement, in spite a PP with of + NP, and in either case a gerund-participial can replace the NP. Notwithstanding usually takes an NP complement (which can precede the head: see Ch. 7, §4.2). In its concessive use, for takes an NP complement beginning with all. Albeit is restricted to formal style, and takes only a verbless clause as complement.
The relevant example is  ii. It is almost exactly like  in that the complement of despite is a gerund-participial clause. One slight difference is that the gerund-participial clause
 there being a blizzard in the area
is also an existential clause (CGEL, pp. 1390–1392). Therefore, in , there is the subject, and the NP a blizzard in the area is a displaced subject.