What does the absence of passive margins between 1740-1600 million years ago tell us about the tectonic environment at that time? In the article Passive margins through earth history (Bradley, 2008), a passive margin is defined as:


  a synonym for the bulkier Atlantic-type
  margin, trailing-edge margin, rifted margin, or divergent margin. A
  passive margin is one formed by rifting followed by seafloor
  spreading, so that the resulting plate consists of both continental
  and oceanic lithosphere, welded across an igneous contact. 


In the research, the author determined that in terms of the abundance of passive margins that the distribution varied with time, from the article:


  They were abundant at
  1900–1890, 610–520, and 150–0 Ma, scarce at ca. 2445–2300, 1600–1000, and 300–275 Ma, and absent
  before ca. 3000 Ma and at 1740–1600.


The absence of passive margins older than 3000 million years is uncertain, possibly due to lack of preservation; however the absence between 1740-1600 million years is described vaguely by the author as being the result of


  One by one, each of these margins collided
  with something, leaving no passive margins at all


possibly related to the coalescencing of the "supercontinent" Nuna - but the total absence is not noted in association with other supercontinents (Rodinia, Pangaea etc).

What does the absence of passive margins between 1740-1600 million years ago tell us about the tectonic environment at that time?
Good paper you reference there.  I think you are starting to answer some of your question by noting that Bradley associates the absence in passive margins with the Nuna supercontinent.  All "rifting" / spreading is taking place in the oceans - pretty much a requirement for supercontinents,  and in this case all continental margins (or at least for those with surviving geological record) were destructive margins.  Over time the duration of passive margins has changed.  For more recent supercontinents you mention, the shorter cycle of a passive margin may have made it very unlikely that tectonic events could cause a simultaneous gap in all passive margins.

As Bradley points out in his conclusions, tectonic activity when Nuna was around may have been globally more sluggish that today, or during the time of Rodinia and Pangea. It may also tie in with the formation of some mineral deposits.  For example, there is a peak in porphyry deposits at about this time.  Now taking into account that older porphyry deposits are less like to have survived (lost through erosion, buried or consumed in later tectonics) the peak at this time may reflect that it was a particularly good porphyry generation time for so many to have survived.  Porphyries do like convergent margins and there would have been lots of those.