I've done a little volunteer go education with kids. as purist I wonder if drawing things out (especially the atari frowny faces, but even the squishy part ) wont build some bad habits around not thinking things through yourself.
but I can't take myself very seriously. I think its much better than the 'capture' approach where we dont explain any rules except surrounding, and the first capture wins.
Stone scoring is equivalent to area scoring (as used in Chinese rules) modulo a "group tax" of two points per separate group.
It's still not a good idea to play inside your own territory as long as there are neutral points on the board. (Except in more complicated situations where it might be necessary.)
There are different rules on scoring, Chinese rules don't care about stones in your territory. Japanese rules do.
From what the page says, this uses the traditional japanese rules (Stone Scoring)