It might be very difficult to get beyond conjecture here, but I would suggest as a possibility that this review of the sixth volume of d'Alembert's independently-published mathematical works could be an early piece by Laplace.
Laplace after arrival in Paris in 1769 had obtained his first post by the help of d'Alembert, and in March 1773, shortly before this review appeared, Laplace had been elected as a membre adjoint of the Académie royale des sciences. So it seems that the young Laplace would have been both eligible to write and publish such a review of d'Alembert's book, and possibly interested to do so.
I do not know whether there are sources of evidence that could help to test such possibilities: Laplace was a successor who eclipsed his early patron, and in later life was also known to be reticent in acknowledging some of his 'roots' and early activities. As Michel Paty has noted in Les recherches actuelles sur d’Alembert (2002), the difficult task of historians of science is to bring out hidden or forgotten contributions by taking away those later 'sediments' that have dimmed and blurred them.