Does it matter if my boyfriend is flirting on Facebook if he never sees her in real life?

[Elle]

I had talked to my friend and she said it was emotional cheating but reading through their messages he made it pretty clear he didn't want to see her in real life .. So nothing really detrimental can happen . I'm SO angry that he's chatting up another female but I don't think he would ever have sex with her. This is the first time I caught him flirting with another girl also

So my boyfriend is flirting heavily with this girl that lives in our city.. How do I know this ? I snooped in his Facebook and read several conversations. It's crazy that he writes her so much. Me and my boyfriend have been dating for 2 years and we see each other almost everyday .. He only facebook messages her.. So I guess I have the upper hand
I have met her plenty of times in real life cause she used to go to school with me but my boyfriend said he's only seen her once and that was from afar. I still haven't told my boyfriend I was snooping on his page .. I don't think I ever will.
So the Facebook messages go like this
The girl : come meet me at the movies
My boyfriend : I can't case.. It wouldn't be right for me to be meeting other girls at the movies .. I know I wouldn't want my girlfriend meeting other guys at the movies .. But one day we will see each other "
The girl : I used just wanted movie company but have it your way

Fast forward to like 5 days and this is how the conversation goes
Girl : you're too lame. It's a problem
My boyfriend : you need my lameness
Girl : I don't know how two extremely lame people could possibly be friends
My boyfriend : you're a living witness
Girl : I'm retiring from my lame ways
My boyfriend : you can't I won't let you . Knock knock
Girl : who the hell is there
My boyfriend : you was lame enough to come to the door though
Girl : you make me cry everyday .. I hate you
My boyfriend : you not crying first of all. Second of all, I make you a happy go lucky person