I didn't actually watch the video, but I have read the original essay and I thought I'd offer a few thoughts (and criticisms) of it.

An interesting consequence of his strict utilitarianism is that it follows from it that it's actually immoral to do anything to help issues close to home in pretty much any way if you live in the West, and maybe even in other countries as well, regardless of whether that may be by donating, volunteering, or anything else of the sort.

if it is in our power to prevent something bad from happening, without thereby sacrificing anything of comparable moral importance, we ought, morally, to do it.

Because of wealth disparities between countries, your money will almost always go further somewhere else. If you live in the West, this difference can be extreme, and as a result any money sent there will be able to accomplish far more than it will for people in your own area. Since your donation to help out nearby is a donation not being made elsewhere where it can do more good, it is then to be considered immoral. A similar logic can be applied to volunteering. If when you're volunteering you are not working to make money which you could donate to much poorer countries, it's immoral, because your personal work to do good will never be able to equal what your money could do. In fact, your life should essentially be, to the greatest extent that doesn't reduce the amount you can make by the harm it does to you, you constantly working. He even admits as much:

Given the present conditions in many parts of the world, however, it does follow from my argument that we ought, morally, to be working full time to relieve great suffering of the sort that occurs as a result of famine or other disasters.

He even goes as far as to say the following:

we ought to give until we reach the level of marginal utility ---that is, the level at which, by giving more, I would cause as much suffering to myself or my dependents as I would relieve by my gift. This would mean, of course, that one would reduce oneself to very near the material circumstances of a Bengali refugee.

If this is the case, it has important implications for political action in its many manifestations as well. Should I be campaigning for the government to adopt policies which reduce suffering as much as possible? If implemented their effect could be massively beneficial, but I don't think this works with the arguments he makes. My individual contribution to a political movement will never be the difference between its success and its failure, so it would seem the moral decision is for me to remain effectively apolitical.

This however strikes me as being in contradiction with this later statements:

I agree, too, that giving privately is not enough, and that we ought to be campaigning actively for entirely new standards for both public and private contributions to famine relief.

I would sympathize with someone who thought that campaigning was more important than giving oneself

Ultimately, I am led to the conclusion that following his arguments, the only moral thing to do is in fact to relentlessly pursue financial gain, as donating the money one earns is far and away the most effective use of one's time and effort to do moral good. The engineer who could have worked for Lockheed Martin designing weapons for the US military is in fact more moral than the one who turns down the job for one that pays substantially less, since it is practically certain that whoever would take the job otherwise would not donate as generously as they do. Applied to capitalists (the class of people, not the supporters of capitalism), it seems that since giving money is the moral thing to do, and giving more money does more good, making more money is the moral thing to do, as it increases one's capacity to do good. This seems to be borne out by his statements concerning foreign aid, which indicate that it's not just about giving what you can in the present moment, but also considering how your actions impact your future ability to continue to do so:

Yet looking at the matter purely from the point of view of overseas aid, there must be a limit to the extent to which we should deliberately slow down our economy; for it might be the case that if we gave away, say, 40 percent of our Gross National Product, we would slow down the economy so much that in absolute terms we would be giving less than if we gave 25 percent of the much larger GNP that we would have if we limited our contribution to this smaller percentage.

I find that this ends up being quite problematic, because the ability to grow one's own wealth is functionally unlimited. It might seem that that's not a problem if you're giving away all your wealth, but for it to grow so you can give more, that can't be the case, because you need to be reinvesting it. As a result you end up with this contradiction, where your are morally obligated to increase your wealth so you can do more good, but at the same time this obligation prevents you from actually putting that wealth into doing good. You could say that the not doing good with the money means that it's no longer moral so you have to give at some point, but the problem with that is that it's impossible to define that point. It still remains that at any given point in time the moral thing to do is to reinvest it so that if you give it next time, more will be given. Ironically, this endless pursuit of ever greater wealth is the very same thing that creates so much suffering in the world, even if its justification is usually different, so this argumentation seems to just end up reinforcing the same ills that it hopes to address.

I do like his conclusion though, directed towards other philosophers, reminiscent of a Marx quote that I've always been quite fond of: "The philosophers have only interpreted the world, in various ways; the point is to change it."