Kroger isn't the only one that claims to not take any other payment type. I had an incident at Wally World, it went through. As to the OP's original question, I have used it there. I got the spiel of we don't... as I was putting my phone on the terminal and to the cashier's surprise and her neighbor, whom she had called over to to query whether Samsung Pay was accepted, it went through.
To Insp_Gadget, while this in theory is correct I've had several incidents where this didn't hold up. I'm not sure what is actually required but some places really can't take it. I've found that many of the places that have card readers attached to tablet type registers seem to be the main ones. There was also a time at the movie theater with a kiosk with a card reader like on a Redbox.