Don't get too hung up on "the first definition". The first definition of product in M-W is "the number or expression resulting from the multiplication together of two or more numbers or expressions". That says absolutely nothing about what it means in any particular sentence.

The bit rburhum objected to says "We're not trying to make money. We're testing a product right now." This is correct idiomatic use of the word "product" (in the sense "something we make"), and it's a relevant answer ("we don't have one") to the question "what is your business model?".