A lot of the things from the video are just trying to create a problem where there is none. Nobody controls the internet; people only control their platform on the internet. Google controls Google and all their other services. So if you decide not to use Google products anymore, you will use something else.
Now I would like to ask, whose platform is the new one? Isn't it the same corporations? Or the governments of Africa and the AU? Either way, both situations are not looking good.

If it's owned and controlled by corporations, then there's no difference with Google.
It's even worse if it's controlled by the government. Africa has one of the worst, if not the worst, governments on earth. They're known for having dictators who refuse to leave office, or have respect for human rights; they do whatever they want and find ways to enrich themselves without thinking about the development of the country. Is this the kind of people you want to hand over the control of the internet to? I think not.

Some might argue that the West are their puppet master and they do all those horrible things because it's what the West wants. If this is true, how do you think the West would let them do something like this?

If we are to have a war with Google, Microsoft and every other big tech corporation, the war should be on privacy and not this. I don't know if it's like that all over the world, but every Android phone that makes its way to Africa automatically comes with Google and most of its services installed. The primary apps (in-built) of the phone are Google products. This is most likely a deal they have signed with the companies that produced the phones.  The same can be said for laptops; Microsoft is automatically the operating system of the laptop you're buying.

Believe it or not, the internet won't cost significantly less if they ditch Google. The ISP determine the cost of my internet, not Google, and unless you want to stop foreign companies from going into the continent, it boils down to who can offer the better service. I'm not going to use a product simply because it's African. If it's African and shit, I won't use it, if it's African and better than the alternative, you won't need to tell me twice.