Does next of kin have any rights to life insurance death benefits if not listed on the policy?

This is actually not a straight answer but this is how it works. If the next of kin are not listed as the beneficiary of the policy and the current beneficiary is living; no, the beneficiary of record is entitled to payment from the insurance company. You could take the beneficiary to court to see if a judge will over turn it but it is unlikely that they will because the life insurance contract is a binding legal document. And furthermore the life insurance company is obligated to pay in monies to the beneficiary on record so by the time you take it to court that money would have already been paid out.
If no beneficiary is selected, depending on the state the contract is enforced in, it money could go into probate and you would have to go through the probate process to have access to any funds. Keep in mind that probate opens the doors to creditors/debtors as well.