Hello Carolyn, Sillal et al,
I'm sorry I should have provided more information. If you dig a little deeper on the site you will find they are associated with Chozenji from Hawaii and Chicago. This temple was set up by Omori Sogen Roshi, and one of the arts practiced besides zazen and shodo is Jikishinkage-ryu kenjutsu. They practice the first scroll of the ryu which is called Hojo. Most people of the group simply call their practice Hojo training. One of my Daito-ryu teachers in Japan studied the Hojo with Omori Sogen Roshi. I think Kondo sensei's dojo was even given it's name by Omori Sogen Roshi. It is most certianly an "internal" style of kendo, if such a thing exists. These guys have some of the best breath control and kiai I have ever seen! Being on the other end of the bokuto will make you want to drop your cookies! If I understand the lineage though, Mr. Sogen was a junior line of the ryu. The late Namiki Yasushi (sic?) sensei was the last headmaster.
Check out these links for more information on Mr. Sogen:
http://www.izs.org/newsite/programs/chozenjizen.htm
http://www.izs.org/newsite/about/Omori_Sogen.htm
http://www.shinjinkai.org/ztai.html
For more on Yamada sensei (15th headmaster) check out Draeger's "Modern Bujutsu and Budo," there is a lot about him in there.
To see Mr. Sogen in action the koryu video series (sorry don't know what it's called) has him doing the Hojo and Kodachi scrolls. It's likenothing you've seen before.
And before you discount Shinkendo check out the dojo. I formally practiced the art for two years and what I learned, I am still applying it to nearly everything I do in budo. Obata sensei is no joke! His art is solid and his personal skills are second to none. His tameshigiri is some of the finest I've ever seen! Is it koryu? No. Is it like Koryu? Maybe? Will you be good with a sword after years of study? Ohhhh Yeeeaaaahhhhhh!
Enjoy!