The Paradox of Thrift is a Keynesian economic concept that explains how saving money is good for the individual, but is harmful to the overall economy if everyone does it at the same time. The video explains it as a chain reaction. When an individual decides to save their money, they are reducing their spending. Spending is what drives the economy, so if everyone chooses to save, then no one is spending. This can be harmful because if no one is spending, no one is earning either. This is because one person's spending is another person's income. As a result of less pay, many businesses may decide they have to lay off their workers because they are unable to pay them. Less workers means an overall lower income for the economy as a whole, which actually just makes it harder for people to save money in the first place, because they aren't receiving enough money to save. This paradox is an example of the fallacy of composition which says that what is true for the individual isn't always true for the whole group.
The last sentence was good, tying in other concepts.
You made a claim that "if no one is spending, no one is earning either". I can see how according to the Keynesian view one would come to that assumption. But, this claim ignores the whole world of passive income. Like people who own gold, real estate, and are invested in stock. When people invest their savings this is ultimately the most beneficial for the economy because in this way people will gain the most wealth over time without having to spend. The paradox of thrift also ignores the fact that people spend and save money based on their own self interests. It is not selfish to save, it is self interested. Why should people be heavily persuaded and required to spend just for someone else's income to increase and they themselves be worse off?