I do not have 2+ hours to wade thru his arguments. I will give my own thoughts here.
It kind of comes down to your take on scripture, including your view on replacement theology and supersessionism. That greatly influences your take on OT scripture in general, and the Law of Moses in particular. In the OT, polygamy (specifically polygyny) was allowed. It was even COMMANDED in certain rare instances. God did not think it to be the awful thing that most of western evangelical Christendom makes it to be. Yes there were cultural reasons for that like an over abundance of women who were without support; often thru male deaths. That brings us to the place where it would be commanded.
Deuteronomy 25:5
When brothers live together and one of them dies and has no son, the wife of the deceased shall not be married outside the family to a strange man. Her husband’s brother shall go in to her and take her to himself as wife and perform the duty of a husband’s brother to her.
There is no mention if the surviving brother is married or not; but since most marriages were arranged around 7 or 8 years of age and consummated at 13 or 14, the likelyhood of the brother being married is rather high. So he would be commanded to take a 2nd wife, with the caveat that all offspring would be counted as his deceased brother's. Yes he had the right of refusal. BUT if he chooses that route, his doing so is considered an insult to the country, the city and his family. (see verses 7-10)
IF you take the OT as having been done away with, rather than God's instructions on how HE wants us to live, then to prohibit polygyny does not run afoul of that command. But if you consider the OT scriptures to still have instructional value, then you must consider that.
2 Timothy 3:16
All Scripture is inspired by God and profitable for teaching, for reproof, for correction, for training in righteousness;
When Paul wrote that, there was no NT, as it was just starting to be written. That means the "scripture" he refers to is the OT, including Deut 5.
OK, what about this scripture?
2 Samuel 12:8
I also gave you your master’s house and your master’s wives into your care, and I gave you the house of Israel and Judah; and if that had been too little, I would have added to you many more things like these!
Or this one, which describes what "into your care" included:
Exodus 21:10
If he takes to himself another woman, he may not reduce her food, her clothing, or her conjugal rights.
IOW, he has to have regular sex with her. God's command.
So what does the NT say, specifically about polygyny? Only this:
1 Timothy 3:2
An overseer, then, must be above reproach, the husband of one wife, temperate, prudent, respectable, hospitable, able to teach,
1 Timothy 3:12
Deacons must be husbands of only one wife, and good managers of their children and their own households.
Titus 1:5-7
For this reason I left you in Crete, that you would set in order what remains and appoint elders in every city as I directed you, 6 namely, if any man is above reproach, the husband of one wife, having children who believe, not accused of dissipation or rebellion. 7 For the overseer must be above reproach as God’s steward, not self-willed, not quick-tempered, not addicted to wine,
Nothing else is said. YES I agree that the Genesis says the ideal is one man and one woman. It also shows the ideal is that we all are "naked and unashamed." Things changed with the fall. Life is not that ideal anymore. God made allowances. The ONLY place where polygyny is prohibited is for congregational leaders; elders (includes pastors) and deacons.
In conclusion, is it biblically prohibited to New Testament believers? Unless you are (or aspire to be) congregational leadership, NO. But is it advised? Again, NO.
Then there is a whole other argument, that it is against the civil laws of the country and states/provinces. And we are instructed by BOTH Paul and Peter in the NT to obey the laws of the land (remember Nero was giving the laws at that time) and to not do so was to disobey God.