No, that is not the definition of a Ponzi scheme. A Ponzi needs funding from outside money to continue to operate, but not everything that needs outside funding to operate is a Ponzi scheme.
As an example let's create a gambling system. Any deposits made into the house account gives you a proportional share of the profits of the system. If the house gets lucky investors can make money. If they are unlucky the house account can run out of money and require outside money to work again. This gambling system isn't a Ponzi scheme at no point are you paid out with new investor's money. If you are lucky you are paid out with gambler's money and if you unlucky your investment goes to 0.
Edit: Even with a positive house edge the house can get unlucky and go bankrupt.