Is this girl playing with me? Why does she do this?

As a female who has dated several dudes at the same time I can tell you she is behaving this way because she is not that into you nor does she respect you. It's pretty sad that she isn't even bothering to hide the fact that she is seeing other guys, I feel like in a suddle way she is putting it on the table that she is openly dating and that if you continue to talk to her you are accepting and ok with it. From my experience, it's not wise to 100% give yourself, all your emotions, and love to someone when they haven't even proved to YOU that they feel the same way.especially when it comes to someone who has difficulty committing to one person which she seems like. People like that tend to devote themselves to a person who is hard to read, makes themselves unavailbe to them, are mysterious, and are 'stingy' with complements and showing how they feel about them. I have dated a few really great guys who were so generous with their emotions to where it just felt boring. But its always the guy who plays hard to get that catches my interest. If I was your friend I would tell you to move on with your life and stop wasting your time. It might even be a good idea to start talking to other people yourself. She is clearing stating that she is NOT commited to you, so you should do the same. You are not going to gain her by showing your devotion to her.

Perhaps because after 6 months of knowing each other, she's sick to the back teeth of waiting for you to ask her out officially and exclusively?

Your both using each other.