The internet blures the line between interpersonal and impersonal relationships. It's interpersonal in the sense that an exchange of ideas goes on, people learn the (presented) personalities of those they're dealing with, and likes and dislikes form. It's impersonal in the sense that there is no real accountability, that people can pretend to be who they're not (though we do that in real life too), and that it's easier to write off things said since you don't "know" the person. It's an odd combination, with nothing but words as the medium of communication. All non verbal communication, all feedback from the person you're communicating with, is cut off.
Despite the mix of characteristics, I think that the internet can be a source of interpersonal relationships, much like pen-pals were in deprived centuries past. This isn't all that new, it's just in a new form.
The question, is this the real world, is fairly simple. You're engaging in it, putting time into it, putting your thoughts and (sometimes) feelings into it. It is part of your real world. What part you allow it to play can vary. If you allow AT to be so important to you that a flame sends you into tears or a 1 on your ratings makes you determined to get revenge, you need more interaction with people in the "real world" who are responsible for their actions. On the other extreme, you can totally not care and make yourself a healthy life without regarding anything ever said on AT. You are disregarding (for the most part) real people though, and it's your prerogative to do so, just as you do in everyday interactions. Basically it comes down to individuals, do you use AT to form interpersonal or impersonal relationships? It's a little risky if you're forming interpersonal relationships because the people you're forming them with have no responsability or accountability and you should always have other relationships that incorporate that.