I'm not exactly sure that it is the same type of Shintoism that is practiced in Mainland Japan however..They do believe that a spirit will inhabit Rocks and trees... That part is consistant with Shintoism... Also for instance they have Shinto Kamidana rituals at New years and follow those traditions.. But my ex wife and Senseis over there would always say that it was Okinawan Religion.. A bit different from others...I guess sort of how a Catholic and a Babtist believe in the same God basically but in completely different view points..
I think as far as the Zen Buddism in the Dojo that you are also correct, and I point to Musashi's Book of 5 Rings (Go Rin Sho) particularly to the 21 precepts spelled out in "The Way of Walking Alone" as more of a mindset in the Dojos over there... In other words, they don't speak much during Class.. They come in to train and only that... After class Socialize, but during class, only do..Which I believe lends itself to the intensity level and concentration and focus during training... Very strictly enforced.. I once asked Shinjo Sensei "Why?" about something he taught me one night and they nearly had to call an abulance for me after he showed me why...LOL Never do that again..