'Tee' is what the original form of karate was once called in its birthplace, Okinawa, in southern Japan. The traditional form still practiced to this day in Okinawa, is not about trying to defeat an opponent or becoming a winner, but instead to fight oneself. More than 5,000 visitors from around the world visit Okinawa each year to learn this form of karate. This program follows two of these people, an Englishman and an Italian, about their experiences and how they struggled with themselves over one summer.
Guys. No need to freak out about his pronunciation. He's not saying 手 (te as in karate). He's saying the Okinawan word for hand, "Ti," and pronouncing it correctly. They're two different words from two different languages. Which is why the video is titled "Tee - The Spirit of Okinawan Karate," because "Ti" was the predecessor to "Toude" (唐手 "China hand" also pronounced "Karate") which later was written the way we know it today, 空手, the first character still pronounced "kara," but now changed to mean "empty" instead of "China." This was done when it was brought to Japan, in order to disassociate the martial art from China.

As a side note, the Korean martial art Tang Soo Do, which descends from Shotokan Karate, is still written 唐手道 (Tang obviously referring to the Chinese dynasty).