Well said.
Increasing the supply of good A does not increase demand for good A. That is not what Say meant. Increasing one's supply of A at the same time increases one's aggregate demand for all other goods.
New products with a positive market value were created that did not exist before. Since the only thing that limits one's aggregate demand is ability to pay, not willingnes, increasing ability to pay for additional goods and services also increases demand for them. Thus producing stuff "worth" X (on the market) also increases demand for all the other goods by X.