just playing the devils advocate here... but uh... how do you have a race in a game where you don't even choose an avatar nor add characteristics to it? its all predifined variables. unless you were going out of your way to let someone know your "race" then it's not existent in a digital context.
You can talk about things associated with race, but race itself is a physical characteristic... and hence talking about race or being offended by something with regards to race when no one can see you, would in fact mean that you are identifying certain traits with a specific race as well.
This in itself is called stereotyping, which is generally the issue that is at the heart of all race/ethnic issues... associating all of a group of people based on the actions of few.