What transforms a beer into a Barley Wine? Is it merely high alcohol content or some change, alteration or addition to the brewing process, mandated by law or otherwise that requires the brew be called Barley Wine?
Barley wine is a style of beer: it isn't something that is made using beer as an ingredient (as you might describe whisky).

There are a number of varieties of barley wine (some hoppy, and some with almost no hop characteristics), but they all have a relatively high alcohol content compared to most beers.  The alcohol is produced via fermentation, the same as any other beer, and without distillation.  Note that not all high alcohol beers are necessarily described as "barley wine" though.

As for the legal aspects, I don't know of any regulations that specifically target barley wine.  The law usually deals with alcoholic beverages based on the alcohol content, and from that point of view barley wines would usually be treated similar to normal wines due to the similar ABV.