<human>: Can you condense the text into three sentences or less?

I've been on two (official) dates with this girl. From the very start she seemed into playing the game a little, meaning she wants to appear unavailable (let's call it hard-to-get). I haven't let this bother me a lot, because she seemed really into me during the dates, asking a lot of questions/even casually mentioning future plans for dates with me etc. She also is receptive to anything I do physically and she seemed to enjoy it.

In our texting communication, she's so far took quite long to respond to every message I sent (it was always within 24hrs, though). We also never sent a message more than once a day. However, trying to setup our third date now. I texted her saying I wanted to meet somewhere next week. She replied saying she's booked full that week, and counteroffered a day in the week after it.
However, I've replied saying that day won't work for me and proposed two alternatives.

Haven't heard anything for 2-3 days now. Now, I'm well aware that she probably wasn't booked full at all and simply wanted to seem busy, whatever. I've gotten used to some game playing. In fact, if she hadn't counteroffered, I would've given up on this girl on the spot.
The counteroffer seems to imply she's still interested, but her lack of response after it is a bit confusing, because it implies that she wants nothing to do with me anymore.

Am I interpreting this situation correctly? Frankly, this is THE most hard to get girl I've had to deal with. Bar some very subtle signals from her, any sort of escalation or progression of this thing has been entirely up to me. The only thing she has initiated is actually our first conversation in a bar.

I'd appreciate any sort of input on this situation. I know you are not mindreaders, but I figured some outside perspective might be useful. Also, I should mention that I'm dutch and she's american. Maybe her behaviour is more common among american girls?
<bot>: Very guarded (perhaps just playing hard-to-get) girl suddenly no response. In person seems into me. When not on actual date she seems aloof (texting/response times). Game playing or lack of interest?