What you copy / pasted is a good summation and it's worth noting that what that is referring to are the 5 branches of philosophy: metaphysics, epistemology, ethics, politics and aesthetics.

Metaphysics: the nature of reality and our relationship to it.
Epistemology: how we acquire knowledge.
Ethics: how we should behave / act in a given situation.
Politics: how we relate to and interact with one another.
Aesthetics: art.

The reason for the political view that capitalism is moral rests on the premises established below. Like I said, the branches are hierarchical. You can't form an ethical system, for example, without having an understanding of epistemology (otherwise how would you know what is ethical or not?) and you can't form a basis for epistemology without knowing what it is reality.

So objectivist politics comes from the fact that reason is our means of knowledge and that we have free will. This means that in order to survive as a human being, we need to think and to act. Thought and action are fundamentally independent processes. That doesn't mean we can't collaborate, it just means that a group acting in unison requires the individuals within that group to engage in action and it means that there's no such thing as a "collective brain". People "putting their heads together" are people thinking independently, communicating and using that process to further individual thought and communication and collaboration.

That leads to the question "what is the 'correct' system of politics?" The answer is a system that protects the individual's right to think and act freely. Free of what? Free of force and coercion. Force is the opposite of reason. If you have a system that protects your individual rights to think (freedom of expression and conscience) and act (freedom to acquire and own property, freedom to assemble, freedom of association etc.) then what you end up with is capitalism. Free markets are the consequence of a system that protects those rights.

And yes, objectvism rejects altruism as a moral system. It is important to understand the terms, though. Colloquially, people tend to think of altruism as benevolence and kindness. Philosophically what it means is that a moral decision is always to place the interests of others before your own. Following that to its logical conclusion, if given the choice to feed your kids or someone else's, it would be selfish to feed your own. To paraphrase something Ayn Rand said: "It is not an altruistic sacrifice to spend your life savings on a medical operation to save your wife's life. It is altruistic to give your life savings to a complete stranger and to let your wife die." Objectivism views altruism, as a moral framework, as unfit for human survival because it is a system that ultimately demands suicide. It is never right to do something for yourself when you could kill yourself for the sake of another. Give your food, your clothes, your savings, your life to complete stranger at your own expense. This is where objectivism tends to get controversial because the most common ethical systems are altruism-based, which teaches us that there is no such thing as "rational self interest", that doing anything for ourselves is immoral, that we should be using our lives to serve others instead. Objectivism views life as an end in itself, not a means to someone else's ends. In other words, you're not a tool. Your life has as much value as anyone else's, and it should have the most value to you since it's your life.