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The first series of screenshots (where the battery is at 65%) is much too early to allow for useful analysis. If the need arises in the future, be sure to let the charge level drop to around 30% (as you did in the second set).
Unfortunately you did not include one of the most important data points - you need to include a screenshot of the Screen On details. It would also be helpful if you mention where you keep the brightness level: the brighter the screen, the more battery will be used.
In the History details it appears that you had Wi-Fi turned on the whole time, but you weren't actually using Wi-Fi - you should turn it off if you're not using it, as that will save some juice.
You can't really tell what your Mobile data signal quality is like (unfortunately the icon doesn't show bars or anything similar, and I'm not aware of an app that allows you to track it) but just be aware that Mobile data uses the most power.
Finally, you mention that the phone was getting hot - that's generally not a good thing for any kind of electronic device. I realize that many games tax the CPU and GPU, so if possible you should turn off other things that draw lots of power (like Wi-Fi and/or Mobile data) to help reduce the heat debt and power consumption.
There are apps that you can use to track power usage and what might be keeping the phone from sleeping - here are a couple:
GSam Battery Monitor Pro
http://market.android.com/details?id=com.gsamlabs.bbm.pro
Wakelock Detector
http://market.android.com/details?id=com.uzumapps.wakelockdetector
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