Any one can fork a coin. Then attach a significant market value to the given fork by promoting it heavily. Or if required they can do it after the fact - They can be on the buy-side and creating an ever increasing bid to pump the fork.
As for the support, you will have human greed play a big role. Everyone holding x coin gets 1 x coin + 1 fork coin with significant value which means it will create some market as well as intice miners to mine a coin with much smaller difficulty.
You can't just make random forks and have them be worth something. This is the culmination of years worth of debate and has a significant community following.
The market value of a coin isn't limited to a strict mathematical function of mining power or exchanges backing it. That's the point Matt is making.
Code fork: taking the source code from one project, modifying it, then offering the result as a new project. This is what the overwhelming majority of altcoins are. For example Litecoin is a five-year-old code fork of Bitcoin. Even though Litecoin's code is nearly identical to Bitcoin's, Litecoin from the beginning created its own blockchain, which shares no data with Bitcoin's blockchain.
Chain fork: taking the blockchain from one project, and adding new blocks to that chain that are not compatible with the chain's original style. Variations of this are soft forks (the block-adding rules are made more strict), and hard forks (the block-adding rules are made less strict). Both this week's BTC-BCH fork and last year's ETH-ETC fork were hard forks.
Complications: obviously, a chain fork requires changes to the relevant code to be able to work, so a chain fork usually comes with a code fork, but not necessarily. For example, theoretically, a completely new code base could be created from scratch in a clean-room kind of environment to add new kinds of blocks to an old blockchain.
No, this has been done a number of times. Clams, lumens, byteball, this thing: https://bitcointalk.org/index.php?topic=1883902.0 all come to mind.
It isn't done often because it's not seen as a useful technique mostly: you just gave a ton your asset to people who think it's worthless, and who may actively dislike it. Not a great way to maintain a market price.
Also isn't that splitting hairs about requiring the blockchain history? I don't think Matt said that.
Also if you do share history, it is much much harder to start, because you start off with the previous difficulty which is very hard to mine on. If you start a new altcoin with a clean history, the difficulty starts off very low.
Bitcoin Classic and Bitcoin XT have not actually forked the blockchain. So they are not separate coins yet.
You need to fork the code (with your changed rules) anyways and you can adapt the difficulty then. Bitcoin Cash did exactly that. They lowered the difficulty to something like 10% of Bitcoin anticipating 10% of the hashing power. They only got 1% and there was a gap of 9 hours without any new block. They seem to be at ~1h per block now. [0]
That's completely counter intuitive to what you're saying about Matt's example not having a history.