Of course she is playing games. Everyone does, and those who claim they are not are just playing a weaker game than those who are aware of it.
She wanted to USE YOU for sex! Jeez, open your eyes!
You turned her down, and it seems you haven't obliged her as of yet, if I am not mistaken.
This is why she started to back off.
She told you she had canned all the other guys (of course she has not!) to see how needy you were, whether you were going to want to jump into a relationship. Not sure what you said here but this would have been her prompt to rebuff you. (Becasuse right after she then told you she "wanted to be single for two months". ??? hahaha! I love women!)
It seems you didn't play up to this. So she remained interested in using you for sex. But still you didn't oblige! So, now, she has resorted to playing more hard to get. She was obviously very horny on the first few dates, and very attracted to you, but you failed to read her signals and thus she has resorted to new ones, which again you are not responding to.