K.Y. Tang is a geophysicist who is known for work on the Allais effect, which is pathological science dating back to the 1950's, when Allais claimed anomalous effects on a Foucault pendulum during an eclipse. A Google Scholar search shows no citations yet to Tang et al.'s February 2013 paper claiming to have measured the speed of gravity. As is often the case with pathological science, there seems to be a certain set of people who take the subject seriously and cite each other's papers, while people outside their circle can't be bothered to debunk them. This particular subgroup includes kooks like van Flandern, who has claimed, for example, that light propagates faster than $c$.
As discussed in the answers to this question, we have strong indirect confirmation from binary pulsars of GR's prediction that gravity propagates at $c$, whereas attempts at a direct measurement have been thwarted by the lack of any test theory that predicts any other speed for gravity. As with the previous bogus claim by Kopeikin, Tang et al. seem to have made no effort to seek the involvement of anyone competent in general relativity to help with analyzing and interpreting their data.
A Google Scholar search shows a couple of papers, Amador 2008 and Duif 2004, that reference Tang's previous work on the Allais effect.
Amador, "Review on possible Gravitational Anomalies," 2008, http://arxiv.org/abs/gr-qc/0604069
Duif, "A review of conventional explanations of anomalous observations during solar eclipses," 2004, http://arxiv.org/abs/gr-qc/0408023