As far as I can tell there is nothing particularly interesting about this implementation. It's cool because it lets you play with it and because the code is pretty short which makes it easy for anyone unfamiliar with the algorithm to grok how it works. It also has some nice documentation: http://www.matthewtrost.org/projects/astar/documentation.htm...
Actually, I found the documentation reasonably poor. It does a good job of explaining the API but does little to provide a would-be user with any insights into why the search works, how it works or how efficient it is. It doesn't even discuss why (or when) I might choose one of the three given heuristic functions over the others.
i.e. despite its length, it's not actually a very useful document.
While I agree that what you listed would be useful to include I think it's important to note that it is documentation of his implementation (what the various parameters are for) and not of how A* works. To that end he did a good job. I especially like the little ideas he throws in under "Extending astar.js." He links to the Wikipedia entry for those who want to know more about how A* works.
Suppose the C++ STL documentation, such as it is, linked you to CLRS. Would you regard it as adequate or would you demand more? I don't expect a rigorous academic treatment here but at least something to tell me (a) how efficient the implementation is and (b) why (or when) I might want to use X or Y provided feature over Z. For example: why is the Euclidean heuristic "slow"? Is it a shitty implementation? Is it because it's underestimating the goal distance too much? Another gripe: the author doesn't even tell me what kind of open and closed list implementations are in use!
I don't mean to be a hater but this fails at contributing something novel (which it doesn't), it fails as a learning resource which teaches something interesting (which it doesn't) and it fails as a well documented programming hack (which it isn't).
For the Python programmer here is a very short implementation of A* that someone on Stack Overflow posted: http://stackoverflow.com/questions/4159331/python-speed-up-a...