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.
There is no significant difference in preparation between barley wine and any other strong ale, some barley wines are made with OG's as low as 1.062 (Smithwick's) and the main characteristic is they have very strong kilned malt flavors.
In my opinion Barley Wine is to Malt, what an IPA is to Hops.
A key distinction between barley wine and other strong ales is the presence of residual sugars. When made right, the yeast will be unable to finish fermentation due the high alcohol content. The remaining sugars should then provide the complex fruity/malty/toasty flavors mentioned in the bjcp guide.