Shotgun king has a “throne mode” where you need to pass 12 levels on a row to get some sort of ending. But to be honest it does not have a lot of story, so you can count it as endless run as well. It’s more the way of playing, where each level you pass you get to choose two random modifiers (good and bad) for the following level.
You also get additional weapons and modifiers each time you get to the ending and we haven’t yet seen all, so it has reply value and maybe an extra ending 🤷♀️