When people think of gangsters, they would normally think of the classic 1930s mafia gangster kind of character. By definition of the word, anyone who is in a gang is a gangster.
There are a few good games based around gangs in the 1920s and 1930s, but it is not something that is easily executed. Modern gangster games are much easier to implement and Grand Theft Auto style games have done a great job at taking the idea of a modern gang and building a successful game around it.
