They do. Sort of. Amazon Vine is the system you're looking for, I don't believe the reviewer gets paid directly but they do get the thing they've reviewed for free (presumably they could then go on to sell on Ebay or indeed Amazon itself). Amazon also points out it was a Vine review when you're scrolling through which is great as it means you can more easily ignore the biased reviews.

https://www.amazon.co.uk/gp/vine/help