The meditation is called "Chinkon". It is based on zazen and breath control. During this part of the practice, the kenshis recite a text explaining the essence of Shorinji Kempo : the Meditation (Seiku), the Oath (Seigan) and the Creed (Shinjo). You can read this text here
You can also read some philosophy speeches Kaiso was giving at Shorinji Kempo seminars in Japan.