That definition more accurately fits the typical usage of the term 'dork'. The word 'geek' is usually used to indicate someone with a great deal of specialized knowledge (such as a computer geek, or a math geek, but also sometimes less technical topics, like a literature geek or a band geek), and typically a lack of social prowess. A 'nerd', on the other hand, is more typically one who displays heightened scholastic ability in all (or at least most) areas, but a significant lack of social skill.

I'm not trying to say that any other use of these (or any other) words is, in any sense, wrong. But these are their current, common, usage.

EDIT (since the urban dictionary link wasn't there when I wrote the above): Remember that different people use words differently. An urban dictionary definition is just what the people who use and vote on urban dictionary definitions (in particular, the urban dictionary definition in question) agree that a word means. This is why lexicography isn't trivial; there is significant sample bias in, for example, the set of people who care enough about how urban dictionary defines 'geek' in order to change it.

This is a linguistic tar pit from which there is no escape. Run away while you still can!