This is an interesting question.
What you have described in your girlfriend is what some relationship experts call, emotional cliff hanging. This is where a person associates the feeling of excitement and emotional uncertainty as a powerful attraction. They like this feeling (kind of like a roller coaster junkie getting a "high" from a particularly scary ride). But, they fail to see that in a real relationship, if this is done on a consistent basis, it actually causes and brings about real instability.
Indeed, this is gamesmanship. And clearly you feel you need a much more stable and realistic relationship. I don't blame you. She is acting very adolescent and while a bit of this might be fun, the level she expects is not.
Certainly this type of emotional play can be enticing at times. But to do so to the level she is expecting is not usually viewed as a good thing. Usually people who crave this type of excitement have grown up in emotional chaos and feel they need these feeling to feel "alive".
I might consider asking her to place some limits on the behavior as it truly is not building up the relationship as it presently stands. But, importantly, you are not wrong here. This is a bit too much for an adult relationship and when done consistently over time will drive apart a couple. She needs to be more realistic about what stability really means. Steven