It is not one kind of book but a collection of around 20 texts, all covering the life and death of the virgin Mary, but quite different from each other. It is more properly called Transitus-Mariae-literature, part of a large medieaval tradition.
Compared to other apocryphal books they are commonly dated quite late, but the exact dates or even order of dates between them is not readily apparent:
This article discusses recent attempts to classify the early transitus texts and to determine which group of texts is the earliest. The Syriac Obsequies, which belongs to the same textual family as the Greek R and related texts, is of crucial importance here. This family emphasized Mary's fear of death and described her assumption to a paradise separate from heaven, where her body was placed under the tree of life and the soul replaced, a descensus followed, describing the visit of Mary and the apostles to hell and, perhaps, heaven. The development of the tradition is traced through R, the Latin texts and the Old English narratives.
Mary Clayton: "The Transitus Mariae. The 'Tradition and its Origins", Apocrypha, Vol 10, 1999, pp. 74-98.
If the author of that lecture is correct in equating 'Abdan' being Abdagases then he seems to make quite an early connection as Abdagases as he "ruled during the first decades of the 1st century AD." Note though that this is a stretch and even if correct it only shows a literary connection, in themes, not a date of these texts.