I preface this by stating I am an atheist, and I have a huge interest in these kinds of morality debates.
That video fails to add anything new to the conversation, and has the annoying habit of setting up weak arguments, and destroying them. "Society 1 villifies children as witches..." "Society x refuses to educate women, who support this position themselves..." I mean, that's pretty weak, but it seems good because it's presented so concisely and clearly: and to be fair, the presentation and points are taught, clear and presented well.
But it makes several assumptions that weaken it, and it's set-up of arguments is one of my least favourite methods of arguing a point. Using examples (even invented ones) is of course useful for illustrative purposes, but this fellow seems to be arguing as to why certain societal set-ups are immoral, when few of those exist. The closest one to existence would of course be the society which refuses to educate women, and in which the women support this resolution, which we see to varying extents in some Islamic cultures. One of the biggest problems this poses is the majority of people, Christian, religious at all, or atheistic, are going to reject the scenarios as immoral, but this doesn't strengthen his argument like he thinks it does.
It also assumes that he knows the 'correct' approach to morality, which is foolish and arrogant. He alleges homosexuality is not a moral question and is falsely framed as such because it causes no harm. I would agree with him, but this doesn't actually remove homosexuality from the arena of morality completely, because we do have people who operate under other moral frameworks. He asserts that you can't accept every other cultural framework (true, although again, his set-up argument is characteristically easy for him to tear down), but the reality is we have to understand them if we ever hope to change them. So we also have to accept that some people see homosexuality as a moral issue. He argues for pursuits through science and logic, which is well and good, but they run up against a wall when people believe you can cause damage to a soul, which science and logic can't help.
Finally the argument about godlessness is less about the basis for morality: we understand that society functions on certain moral rules, but more about the purpose of moral behaviour. If I see someone lose their wallet, should I call after them to return it? Or just take the money? I gain by taking the money, and lose nothing. There's no incentive to be good, so the question becomes, why be good, and even more esoterically, if there is no arbiter of justice, is there good or evil at all.
It's not that I disagree with the assertions the video makes, but I do feel he misses several points, makes some obvious weaknesses, and neatly avoids the crucial question of why or if one ought to be moral in a Godless universe, which can be an infinitely fascinating question, by cleanly assuming that there is a morality which ought to be obeyed.
(As an aside, Christian morality isn't about a cosmic reward/punishment system, either. The Bible explicitly states that if you are only good to avoid hell, or to get into heaven, you are not being good: the goal is to love God so fully that you obey him out of love, and are therefore good.)