Young people say this more often. It's like saying "yeah, i know exactly what you're talking about from my experience" in a short way.

I'm not a native speaker, but as far as I know, when someone tells me "I know, right?" they're telling me "I agree with what you're saying, isn't that cool/weird/etc.?" the "right" part may expresses different kinds of "reactions", like if you are talking about something weird, "right" would be "isn't that weird", but if you're talking about something amazing "right" would be "isn't that amazing?". That's all I could think of. :)

The writer expects that, after the situation has been explained (the first sentence), the reader will feel surprised and say something like "What?" "You can't be serious" "That's unusual" etc. The writer anticipates this reaction and replies with "I know", which indicates agreement with the surprise. "right" is often used at the end of informal statements in order to seek reassurance or agreement.