If I live in the woods alone, hunting and gathering my food and felling my own timber for firewood and construction, then that is my economy. Economy means how a society allocates their resources. If I live in a one-person-society as a hermit, then me gathering and hunting at least enough food to stay alive and having enough resources to keep my abode able to protect me from cold and rain is my economy.
As economy means simply allocation of a society's resources, it is not possible to not have an economy. There is always an economy. But, it doesn't need to be based on money, necessarily. Any system where goods are distributed to people who need them is an economic system.
So, the OP is misunderstanding the word "economy", but the main point of course still stands: The monetary economy as we see it in our current society is actually purely a social construct. Or simply: "Monetary economy isn't even real, we literally fucking made it up" is correct.
But economy is real.