The question is still badly worded. If the question is whether "the Syrian conflict was caused by climate change as the media seem to claim?" then the answer is clearly no, and the media article linked in the question does not actually even make that claim. To quote the author of the study from the Independent article:
“Added to all the other stressors, climate change helped kick things
over the threshold into open conflict,” said report co-author Richard
Seager, of Columbia University in New York.
In other words, it was a contributing factor, but it would be an exaggeration to claim it was the cause. This is also bourne out by a quote from another author:
“Whether it was a primary or substantial factor is impossible to know,
but drought can lead to devastating consequences when coupled with
pre-existing acute vulnerability,” said lead author Colin Kelley, who
did the work at Columbia but is now the University of California,
Santa Barbara.
Now there is another quote from Prof. Seager
“I think this is scary and it’s only just beginning. It’s going to
continue through the current century as part of the general drying of
the Eastern Mediterranean – I don’t see how things are going to
survive there,” Professor Seager added.
However this is not a statement about the cause of the current conflict, it is a statement of how he thinks the climate will develop in this region.
As to whether the science is sound, there have been previous papers on this particular topic, with similar findings, e.g.
Peter H. Gleick, 2014: Water, Drought, Climate Change, and Conflict in Syria. Wea. Climate Soc., 6, 331–340. doi: http://dx.doi.org/10.1175/WCAS-D-13-00059.1
Such replication, where different authors study the same issue and come to similar conclusions, is part of the process to scientific acceptance of an idea that only starts with the publication of a paper in a peer-reviewed journal. So I would say that the indications so far are that the science is probably sound. Of course there are some that are unwilling to accept the findings of studies based on computer models, however the use of such models is widespread in science (not just climatology), without raising similar objections.
Update: There are also indications in the most recent IPCC WG1 report that there are projected hydrological implications of climate change for the middle east, which would be in accordance with the two studies mentioned:
Annual surface evaporation is projected to increase as global
temperatures rise over most of the ocean and is projected to change
over land following a similar pattern as precipitation. Decreases in
annual runoff are likely in parts of southern Europe, the Middle
East, and southern Africa by the end of the 21st century under the
RCP8.5 scenario.
and that this was not a new finiding for AR5
In the AR4, 21st century model-projected runoff consistently showed
decreases in southern Europe, the Middle East, and southwestern USA
and increases in Southeast Asia, tropical East Africa and at high
northern latitudes. The same general features appear in the CMIP5
ensemble of GCMs for all four RCPs shown in Figure 12.24, with the
areas of most robust change typically increasing with magnitude of
forcing change.
Basically I think this is just another case of the media exaggerating a scientific story, but also of reading more into the media article than is actually there. This happens all of the time, because we are all subject to cognitive biases, such as confirmation bias.