"Laws of Nature" and "Nature's God" are terms that are primarily associated with deism.

Washington was well known as a deist, as were most of the founding fathers. You will find that there are no records of George Washington ever referring to Jesus - not a single mention of Christ in all of Washington's writings.

That is important in the context of the modern conservative christian idealogy which is firmly based in revelation. Deism completely rejects the idea of revelation.

Beyond the abstract characteristics of generic monotheism, the God of the deists shares very little in common with the God of christianity. For the most part, deists are just one step away from being agnostics.

Given that background, it is interesting that the article you linked to quotes Washington's farewell address in which he said:

"And let us with caution indulge the supposition, that morality can be maintained without religion. Whatever may be conceded to the influence of refined education on minds of peculiar structure -- reason and experience both forbid us to expect that National morality can prevail in exclusion of religious principle."

Note that part about "influence of refined education on minds of peculiar structure" -- basically he just said that enlightened people don't need religion to have morals, but for the average bloke its simpler if somebody else sets out the rules of morality and they just follow along.

I'm pretty sure that the author of the article didn't really pick up on that, despite it being in character for Washington - for example, he attended church about as rarely as he possibly could given his position in society.