What's more, it makes some silly comparisons (horses aren't humans, for instance.) 

It's comparing the economic utility of horses versus the economic utility of people in different centures. Horses gradually "peaked" in economic utility (alongside the rise of automobiles and related infrastructure) far earlier than humans because, erm, they're horses. Humans will peak too, for similar reasons (automation), just far later. Carrier pidgeons also peaked before horses did. 

Anyway, there are limits on what humans can do too, and in 2014, computers have already surpassed us in a lot of ways we once thought impossible to be surpassed in. Analyzing vast amounts of legal and medical data in a way that is more accurate and significantly faster than humans in order to help highly educated specialists make decisions, for example, is one of the more recent things software has been able to do. As of this year, artificial vision systems (like those that drive image recognition) have surpassed humans in our ability to recognize and categorize objects, something which most people thought was decades off. 

Deep learning is opening up more possibilities any day, to the extent that people like Elon Musk and Stephen Hawking are warning people about the looming dangers and existential threat of AI in the short term (Elon Musk recently said that if you knew what he knew, you'd be terrified too).  

Back on the subject, as we go down the list and as more and more boxes get checked off, it's no stretch to assume that the vast number of jobs that are the cornerstone of the economy today (those listed in the video) will be mostly automated in the next decade or two. That's why the horses in 1919 analogy is perfectly apt. Without speculating into the nature of jobs which don't exist yet, I can't imagine a world where people are still brewing coffee and working at call centres en masse ten years down the road. It isn't even up for debate, really as that technology is already here.

You could tell a classroom full of elementary students that none of them would ever have to work at a call centre, in fast food or in transportation in any capacity and you wouldn't be wrong. You could also tell them that most of them will never have a driver's licence and you wouldn't be wrong either.

 

It also makes some silly statements, such as "the human brain isn't creative." It really starts to fall apart in the last third, when it makes a number of complete non-sequiters and unsupported conclusions.

I don't understand why you think that is silly, that is, unless your motivation for saying so is religious in which case I can't help you. 

That argument hinges upon the notion that the human brain is in essence a (wet) computer. It might be the fastest computer we know of with both the most efficient parallel processing and lowest energy requirements of any computer on the planet, but it is still bound by the same laws of physics that all processing power is bound by. There is no "magic" that completes the human brain, and it follows that any sufficiently advanced computer, biological or not, would therefore develop it's own, unique consciousness and subsequent behaviours. 

We've been ever so slowly reverse engineering the brain for decades and this progress has only accelerated over the past few decades. You'd be hard pressed to find someone working in any of these fields who doesn't think we'll be able to emulate a human brain at some point, the only debate is when. Such a brain will surely have it's own faculties, drives, emotion and what have you.

Also we don't have to emulate a human brain at all or even try if we want to replace most people's jobs with software and hardware bots. 

What it's touching on is a field of economics known as "post-scarcity" economics. It's a woefully under-researched field, as it's always been a fantasy (in fact, the only depiction of that kind of economy I can think of is in Star Trek.) While it's fun to think about, and it's fun to fantasize about, it actually can't occur. There will always be something scarce. Even in Star Trek, there is a demand for novelty. That's why we see a society that prioritizes exploration. There are no janitors, or burger flippers. But there is still work to be done by people.

You have a point here but the video in question and the worries about automation are in no way rendered moot by this. There will still be a rough transition period regardless if jobs are automated at a significantly faster than they're being replaced. This is already happening and has been happening for awhile. Many economists are waking up to the fact that automation is to blame for the slow economy recovery and economic stagnation. In China, the government has already internalized this lesson and has made a roadmap to help them deal with it as companies like Foxconn proceed to automate their entire workforce within the next decade. 

Also, observe Amazon, Google, Instragram, Facebook or any other software company: they only employ a tiny, tiny sliver of our total economy yet affect the lives of billions of people on a daily basis with a far deeper reach than any of the companies they rendered (and are rendering) obsolete. Look what happened to comparative behemoths like Kodak who failed to adapt to these new business models. 

Jobs in these sectors will never employ many people yet they will continue to impale other industries in the same way they are doing with the music industry, newspapers, box retailers, television, and any other industry that deals in placing monetary values on what can be made digital. They will soon do the same thing to the transportation sector, education (MOOCs - so people in rural India can get a Harvard style education), the service industry (cashiers, call centre operators, barristas), energy/infrastructure, telecoms, and even agriculture (fully automated farms, synthetic meats), manufacturing (3D printing/robotics), the military (autonomous fighting systems), etc. 

Even if you think the "post scarcity economy" will always be a pipe dream and you may be right, even the things that are already 100% set in stone will shake the foundations of human civilization more than the industrial revolution did and they will do it in a much shorter span of time. The "Internet of Things" will represent greater innovation than anything that happened in the 19th and 20th centuries combined. 

Nothing in that video or in any of the doomsayers prophecies contradict the basic principle 

The video or the predictions behind it aren't a doomsday prophecy. People like me are very optimistic about all this. The problem is convincing people, like I'm trying to do right now, to take action before it wreaks massive damage in our economy.

I'd say that the "%45 of jobs will be automated" prediction in the video is very hard to deny if you examine the technologies that seek to replace each job on the list and where they are presently. The only demand for human workers in these fields once automation is well underway will come from nostalgia and a desire for "hand made" goods and services that require a human touch. That demand will be small in the greater scheme of things as, wouldn't you know, most people prefer things to be as cheap as possible and that will mean things that are made by a machine.

that increased efficiency and productivity lead to increased demand, which leads to the need for people to meet that demand. That's not antiquated any more than the law of gravity.

This is missing the point. 

Look at automated vehicles, for example. They don't have to stop at intersections as they can communicate with every other car which means that thousands of cars fly through the same intersection all day at full speed in all four directions and never hit each other even if that means only avoiding other cars by a fraction of a second. These cars also never get drunk or distracted or even crash at all (unless an evil wants them to crash and programs them to somehow). 

What possible good could human drivers do in such a system? It doesn't make human drivers more productive or efficient, it takes them out of the loop entirely in the same way automobiles took horses out of the loop. I could give a similar example of equal weight to every job on the list the video presented. 

You could argue that it will just create more economic incentive to create more creative jobs. This is partly true; we will be freed up to be more creative and spend more time consuming more media made by more people. The thing is that such an industry could never provide nearly the same amount of jobs. 

I honestly can't think of any hypothetical profession that could fill this massive void that will be left in automation's wake. Can you?

Humanity isn't going to be replaced, because when technology displaces us, we simply find somewhere else to concentrate our energy and productivity. And the technology will always be one step behind the people.

The only way technology is always going to be "one step behind the people" is if we merge with it. That may sound like science fiction but when the time comes that might be the only way in which people will be able to keep up and when I say "merge with technology", feel free to use your imagination and guess what that implies.