I can't think of any 13.3 inch laptop that can game. The smallest I know of is 14 inches unfortently. Is there a reason why it has to be this small as you can get light 15.6 inch laptops that can game and have better cooling?
This is not a gaming laptop, it is a laptop that can play games. But there are a lot of things wrong with it if you use it for gaming:
First the screen res is too high for gaming but obvisouly it will be turned downed to 720p which then makes you wonder if the high res screen is needed.
Second related to the screen res is the issue of scaling. It is a known fact that windows doesn't deal with scaling on high res screens which means that icons for on the desktop are very tiny
Third is the size. As the laptop is very small and thin, the battery will get damaged much quicker than its thicker counterparts which will make the laptop essentially a desktop.
Apart from that it is ok for general use and a bit of 3d work but I really would say away from thin laptops if I were you.
You should pay attention to what that OP is asking for. I have quoted it below. Note that he is not asking for a 13.3" "gaming laptop". He is asking for a 13.3" laptop that is capable of doing "medium gaming".
I'm looking for a 13inch laptop that's light, thin and portable. It also needs to be able to do some medium gaming (not on high settings, but medium would be great)
My absolute maximum is around $1250
The Zenbook is capable of doing that. For games that have pretty low graphics requirements like LoL playing at full resolution with the GeForce 840m will be fine on ultra high graphic settings. Games that are graphically demand will likely require low resolution when using medium quality settings, So what? Using lower than native resolution to play games will not impact graphic quality that much. Games will look better at 1366x768 or 1600x900 resolution at medium graphics settings compared to 1920x1080 and low graphic settings.
As for the "thin battery", I do not understand where you are coming from when you say it can be more easily damaged compared to a thicker battery. Under normal usage a thin battery is not more prone to damage compared to a thicker battery. If you are pretty rough with laptops like tossing them around on a regular basis, then sure a thin laptop can get damaged. But a thick laptop can get damaged as well. Besides if you are prone to tossing around a laptop, then perhaps a laptop is not an ideal solution for you.