Actually giri (and I don't have the kanji) is different from reigi - it's "obligations" rather than "general dojo manners" - sort of. Or "duty" or something like that. It's kinda like - hmm. My understanding of 'giri' is incomplete, but it carries a lot of weight, and it's a personal thing - like - if I start a dojo, it's MY responsibility to make sure it's up to the standards of the people who trained ME, or they'll get cranky because, since I was trained by them, and my dojo sucks, it's reflecting poorly on my senseis. But that's not quite it, either.. (and, I'm not starting a dojo any time soon...)
Very true. However, the previous examples you gave were things that are identifiable as being matters of manners, rather than fulfilling one's many duties in life. The word reigi in japanese just means "manners", not "manners in the dojo". People who are exceedingly polite are often referred to as 礼儀正しい人 reigi tadashii hito (informal speech), which means a person of correct manners. What is/ins't appropriate to do, how to talk to people, not putting your chopsticks into your rice, those are all issues of manners. Fulfilling your obligations to your martial arts teachers, parents, mafia bosses (far and away the medium that has the most to say about duty and honor in Japan are yakuza films), etc., are issues of 義理 Giri.
You've definitely got a good grasp of what the term means. The definition is a lot less complicated than people think. It's simply a deeply felt sense of duty. It's just that your previous examples didn't have much to do specifically with giri.