Although Mister Donut originated in the US, most of that chain was absorbed by Dunkin Donuts, with only 3 locations remaining (according to Wikipedia). The Japanese chain is easily the largest and is also the largest donut chain in Japan. I think any casual observer would agree that there are at least two big factors contributing to their success here in Japan. The first is shown in this photo. A group of characters has been developed which ended up turning into a flagship donut. The pon de ring consists of a small balls baked into a donut shaped ring. Not only are they easy and fun to pull apart and eat one by one, these donuts are a little more chewy than regular donuts (not sure, but I think some rice flour is added). The website says these were modeled after a Brazilian chewy bread item called Pao de queijo or cheese buns which contain cheese for flavor and cassava starch for chewiness. This ring is also the most recognizable character in what has become a small group of characters, Pon de Lion (photo). I this is a play on words deriving from Ponce de Leon, more for the sound and for any logical connection.
Photo is a web capture for explanatory purposes, copyright belongs to the company.