I don't think this is the likely intended meaning, but I thought I'd add one to the list of random interpretations: 'Ginger' is old-fashioned Cockney rhyming slang for gay.

As a noun, the word "ginger" can refer to something lively or animated. In this context, perhaps someone is referring to himself or herself as part of the local flavor.

I do not believe that is what they said. I have heard people in Hong Kong are called "Kongers". So perhaps they said "Yes, I am a Konger".

Ginger is person with red hair.