Very well done.
For example, if you gift someone a $100 Amazon gift card, but they also gift you a $100 Amazon gift card. Has any gift actually been exchanged? Yes, the sentiment of giving.
Or if someone pays you $100 to eat a pile of shit, and then you use the same $100 to pay them to eat a pile of shit, you both have eaten, but the money is in the same place it started.
In the end, if you paint a big enough picture, all money flow in an economy is circular anyway.