Is there a word for someone who assumes that if they know something then others do, or should too? ?

-The false consensus effect: its a bias, also known as the Consensus bias, for when someone assumes that their own beliefs are the "normal"

-Self centered, lacking perspective/perspective taking, apathy: can be used to relate to the fact that one doesn't look outside themselves or consider others perspectives and therefor what others knowledge/capabilities are

-There isn't exactly a singular word for this sort of cognitive bias in the English language, that i'm aware of at least. Most people would refer to it as "assuming," "judging" or "overestimating" peoples knowledge/competencies

What culture does that person come from? On a large scale there's something called high context and low context cultures. In high contexts cultures, such as Japan, everyone has studied the same subjects from the same books in school, and had pretty much the same experiences. So they can write and talk in a kind of "shorthand" because they do know what the other person does. The US is a low context culture- people study and read different things in school, watch different tv shows (much more now than when there were only 3 tv channels), have different experiences, and mostly communicate in great detail because they don't know what the other person know. If someone is acting like they know what other people know when they really don't, then they are either delusional or being pretentious. 

Patronizing might have been the word to use, but it implies that the person is seeking to belittle the people who know less than he does.  It isn't exactly a superiority complex either. Nerds tend to assume everyone ought to know what they know. Superiority Complex can also come into it as it is the coping mechanism used by many in reaction to being let down or pushed aside.