I would like to know a word to describe someone who is well-versed in the rules of a game, sport, activity, etc.?
I see that your question no longer mentions your nationality (US). I'm British and a commonly used journalistic word for an expert on sporting matters in the UK is pundit.
pundit : a person who knows a lot about a particular subject and who expresses ideas and opinions about that subject publicly (such as by speaking on television and radio shows)
Other possibilities might be brain, egghead, genius, whiz, wizard, guru, master.
"a referee", or "a sports arbiter", is supposed to know all the rules about a specific game and they make sure those rules are followed during a match or competition.
- referee - a sports official usually having final authority in administering a game MW
A connoisseur is especially competent in a field, especially in the fine arts.
A "connoisseur" is an authority in his field, someone who has expert knowledge and training, especially in the arts. A connoisseur may also be someone with an extremely developed sense of taste, like the connoisseur who can identify rare wine by a flavor others can't even detect. Then again, some people call themselves connoisseurs of just about anything they like — pizza, old vinyl albums, even cartoons — because they know so much about it. - Source: Vocabulary.com.