I have never heard the phrase "Jack-in-office" before. There are lots of words that are close to what you explained, but not *exactly* what you describe.

Following the rules very closely, while missing the point of these rules is called "Following the letter of the law, not the spirit." This is a very common expression. To my knowledge, there is no word for a person who does this.

Another word that is close to what you are explaining is "Stickler". However, a stickler generally refers to somebody who follows and enforces the rules **under any circumstances,** not somebody who's missing the point of the rules. For example, a professor who refuses to accept a test because it was turned in 1 minute late would be called a stickler. Stickler is also *slightly* derogatory, but not vulgar. It's also informal.

Some related words from [this thesaurus page](http://www.thesaurus.com/browse/stickler) are "perfectionist", "nitpicker", and "disciplinarian". These are all related, but I think stickler is closer to the word you are looking for.