If you ask her you could ruin the fun flirty friendship you have now. It will put her in the position to worry about how she acts around you in case she gives you the wrong impression. From your description of the evening, she is not romantically attracted to you and is just using you as a friend to take care of her when she is out drinking. If you don't think thats good enough and don't care if she remains your friend then you ahead and confront her, it will probably knock some much needed sense into her. But be prepared that things will not be likely to return to "normal" in the near future, and maybe her friendship means more to you than needlessly making her self-conscious around you.
Just because she likes you as a friend and you want more doesn't make it "mind games"...
edit: oh, just read your post again and realized she isn't a friend at all but just some random girl at a club you've met twice. Forget all my advice, just tell her how you feel, at least you'll know for sure, and anyway, who cares if she rejects you when you hardly know her anyway? Good luck!!