Specifically the section titled "ASPECTS OF THE LATE ORDOVICIAN MASS EXTINCTION POTENTIALLY COMPATIBLE WITH A GRB".
But if you're looking for an article summary, here is the evidence they mention that may point to a Gamma Ray Burst (GRB) as a possible source of the extinction:
Rapid global cooling followed by rapid global warming
Specifically, they say that a GRB may cause the production of NO2, which will increase the opaqueness of the atmosphere, causing cooling.
Some species impacted more than others
They mention that this may have happened, but that they would expect:
planktonic organisms or larvae would more likely be affected than benthic organisms because the former are less shielded from radiation.
Similarly, epifaunal organisms would be more affected than infaunal organisms buried and shielded in sediments.
They go on to say that both of these patterns "may exist".
Differential extinction
They probably say this best:
longer planktonic larval phases, when such can be inferred, are associated with increased extinction probability
The mention that species whose adults live within plankton were completely wiped out. This differential extinction is somewhat suggestive of a GRB.
Summary
Ultimately, there's not a clear and definitive link to a Gamma Ray Burst as the sole or primary source of this extinction event. However, there are some correlations. In the author's words,
clearly additional tests are required
source: Did a gamma-ray burst initiate the late Ordovician mass extinction? (Melot et al).
So, does that answer the question: no; but it seems to me that GRB doesn't explain better the event that unfolded during the late Ordovician than other hypotheses (namely the ocean eutrophization and the continental weathering). Does it discard the hypothesis of a GRB: no; but since there is no direct evidence that it indeed happened at that time, and that we can explain the Ordovician events without, it seems, to me, more parsimonious to think that it didn't.
References:
Brenchley et al., 1994. Bathymetric and isotopic evidence for a short-lived Late Ordovician glaciation in a greenhouse period. Geology, 22: 292-298.
Kump et al., 1999. A weathering hypothesis for glaciation at high atmospheric $p_{CO_2}$ during the Late Ordovician. Palaeogeography, Palaeoclimatology, Palaeoecology, 152: 173-187.
Sheehan, 2001. The Late Ordovician Mass Extinction. Annual review of Earth and Planetary Science, 29: 331-364.
Vecoli, 2008. Fossil microphytoplankton dynamics across the Ordovician–Silurian boundary. Review of Paleobotany and Palynology, 148: 91-107.