This repo is automatically built by the ROS build farm and its output is hosted here: http://docs.ros.org/kinetic/api/moveit_tutorials/html/
The tutorials use the reStructuredText format commonly used in the Sphinx "Python Documentation Generator". This unfortunately differs from the common Markdown format.
The indigo-devel branch should be considered for the most part "frozen" for historical reasons, and new changes to tutorials should be in the kinetic-devel branch.
If you want to test the tutorials by generating the html pages locally on your machine, install rosdoc_lite:
sudo apt-get install ros-kinetic-rosdoc-lite
and run in the root of the package:
rosdoc_lite -o build .
Then open LOCAL_PACKAGE_PATH/build/html/index.html in your web browser.
For deploying documentation changes to the web, Section 3 of rosdoc_lite wiki says that "rosdoc_lite is automatically run for packages in repositories that have rosinstall files listed in the rosdistro repository." This is done about once every 24 hours, overnight.