I think the article is nicely written ( except the equation numbers are missing!) Hamiltonian formulation of General Relativity (essentially dynamics of geometry) is quite a technical subject, probably not suitable for a casual reader. But in any case, this article could be a starter for those who are interested in this formalism. I think it should be published as it is.
The article is well written, but I am not sure it is in a style that is appropriate for an encyclopedia of physics. The author has to realize that the vast majority of physicists have never even heard of the subtle and deep conceptual problems that the dynamics of general relativity entails (and that took four decades to understand until the seminal ADM work). I would urge the author to put himself in the mind of an experimental condensed matter physicist, take a deep breath, and re-read his article. At the very minimum a smoother introduction explaining why things are difficult, what were the key insights in the ADM work that brought the problem to clarity, is needed.