I understand what you're saying now. I've never seen PPP used in that way though. PPP, as I've always known it to be used, is for standardizing over time. In other words, if a McD's burger cost 10 cents in 1950, but it costs a dollar now, we use PPP to determine that a person with $5 in 1950 can buy as much as a person with $50 today.
With all of that said, I'd take issue with a comparison of GDPs that uses PPP in the way you mention. Because, as a country's GDP rises, the purchasing power of a person in that country typically decreases relative to a person in another country (this is caused by many factors, but a major one is increasing regulation), assuming we're working with a standardized currency. So, I can't see how we'd be able to gain an accurate understanding of anything by watching a video like this one, if it used PPP in the way you mention. It would skew toward poorer countries.
Well, there is no one way to "correctly" compare different economies, as prices are quite bad indicators of real value. For instance, if you clean your house yourself it is not counted in the GDP, if you employ a cleaning service it is counted.
I personally think the PPP-adjusted GDP is a better indicator, but different persons can see it differently. I personally see it this way: if country X produces goods this gets counted into the GDP. Let's say the local currency is exchanged 1 x into 1 dollar. Next year the country produces exactly the same goods. But exchange rate have changed, now it exchange 1 x into 2 dollar. Seemingly the economy has grown 100%, but if you look at it in the local currency you have 0% growth.
That's the reason why China does grow in the last years in the video so exceptionally. China actually has pretty good growth since the 80s, but in recent years the chinese government decided to increase the personal wealth of chinese people and therefore tried to make the yuan more valuable. This leads to this exceptional growth if exchanged to dollar. But the actual economic strength was built over many years.
You're right that a strong currency is the sign of a "rich" country. If you currency buys a lot, your personal wealth will be better of someone in a country with lower valued currency. Basically it means, people in countries with high valued currency will buy more goods than the country produces (leading to import being bigger than export), while people in countries with low valued currency basically cannot buy stuff produced in a different currency.