They capture the most valuable sales--i.e., those made with the immediate intent to purchase--and direct those purchasers to the cheapest site in exchange for a commission.
It comes down to a question of what is more valuable to the seller. The blogger may have created the intent to purchase the product but Honey created the intent to purchase from the specific seller. And to the seller, that is far more valuable, especially as a lot of Honey-generated sales may have been sales that would have otherwise gone to competitors.