"they (the carriage makers) ended up going out of business, because they too narrowly defined their markets as being the horse-drawn carriage market"
Or because they were no better qualified to make and sell automobiles than any other large random group of people, had to pay a lot of employees while they were figuring out what to do next, and weren't willing to bet their company on something with maybe a 10% chance of success. Meanwhile, auto startups were being formed by a few guys in a garage, and the ones that were good enough to build and sell a few cars got bigger while the other ones failed.
I've seen markets drop out under several tech companies - for instance, when Microsoft bundles something into Windows and kills the 3rd-party market - and it's not pretty. If there's a way out, it's probably by focusing on what the company *is good at*, rather than some vague marketing idea of what line of business they're in. For instance, AT&T credit cards - at one point they realized that one of the things they were really good at was collecting money from people.
So the RIAA and MPAA really are in a fight for their lives - any radical change in music or movie creation and distribution will result in a market that they're unlikely to survive in, because they haven't needed and don't have the competencies they'll need to compete in that market.