"Swimming Anime" is not a real anime. Not yet.
The PV you see going around is a commercial made by a company studio called Animation DO, a Japanese studio mostly known for subcontracting work on other studios’ projects. (They were involved in the making of animes such as Air TV, Clannad, Full Metal Panic, Inuyasha, K-ON, and a few others.) The studio Kyoto Animation is one of Animation DO’s parent studios and aided in the making of the Swimming Anime PV.
They made the PV advertisement mostly because they wanted to show off how flawless their animation is. The end of the commercial features the text “A new challenge!” The advertisement is real, and it may become a full-fledged anime one day in the future. The project, however, was put on hold by the creators for reasons we don’t know. Theyhave not made any further announcements about the project, nor have they confirmed if the commercial itself was the new project.
Animation DO had revealed that it had a “project in the works” last April, and included a splash image with the announcement. (Pictured below)
On this image is the phrase “Ore to omae no sa o oshiete yaru yo!” [In english: “I’ll tell you what makes you and me different!] This is why some think that the official name of Swimming Anime is Ore to Omae No Sa O Oshiete Yaru Yo.
Animation DO is currently helping work on the anime Tamako Market.