The short version is that Kota was Openweight Champion and Kenny won a tournament and got to challenge him for it. It was their second (and last) singles match. Their first ever singles match was the match that brought Kenny to DDT in 2008, then they became a tag team. The Budokan match took place in 2012.
"The Ibushi match [at Budokan] that was a very unique situation. I'd made a mission statement to do whatever I could to help build this small company up to something bigger than it originally was when I had gotten there. DDT would run a show every now and then at Kurokan Hall back in the day of 2008, and I had seen this small company grow, and they had run Kurokan Hall monthly, then they could finally run ryogoku sumo hall, and then finally in the year 2012 they could run Budokan. Not only that, but we sold it out. And the company had enough faith to put me on top against, you know, one of my best friends and someone that I had done almost all of my greatest accomplishments in Japan with, which was Ibushi. I had thought that there was really nothing bigger than that. It was uh not just on a professional level, but on a personal level as well. I mean how cool is it that you can share your biggest and greatest match with one of your best friends and do something that you never thought that you could do? It’s really the stuff that dreams are made out of. I had thought that there would be no greater feeling in pro wrestling for me than that moment.” (1/19/17 interview with wrestling observer)