I cannot find references concerning the complexity of the variant of the knapsack problem (decision version) where one of the two conditions must be a product instead of a sum (0 not allowed).
A related question is this one: Combining subset sum and subset product problems .
It is well known that we can say that knapsack is the special case of subset sum (where each weight is equal to each profit and the bounds are the same) to satisfy the equality of subset sum with 2 inequalities. However, this is not possible here since there are 2 equalities to satisfy in the "subset sum product" problem and we have only 2 inequalities in the "knapsack sum product".