Money was the driving force behind many things that happened in the American Old West. Those who had money hired hands that had the most guns. Those who had guns ruled cities and towns that sprang up 150 years ago. Although not exactly lawless, the American Old West followed the money first and foremost.
I do think that the American Old West of the 19th century can fairly be considered as an example of proto-anarcho-capitalism. It was wild times and there was pretty much anarchy for sure. Also everyone was out to make a buck. New companies were being started left and right, so yes it is an example.
Yes, the American Old West of the 19th century can fairly be considered an example of proto-anarcho-capitalism, because it was more or less every man for himself. People were still guided by their own morality, and were still able to buy and sell, but there was not a large law-enforcement presence at all. People were basically left to defend their own justice.
I believe it is possible to derive many similarities between anarcho-capitalism and small cities or towns in the American Old West. I believe, in order to do this, you would have to consider smaller communities that are essentially far away from any other communities for this comparison to be truly effective.
The American old west was a time when people were not worried about anything but simply survival and trying to scratch out a living. A lot of the people then were living off what they grew and killed, so while it may be considered this type of capitalism, they were simply living.