Definitely get either the:
MSI G Series AG240 2PE-009US 23.6-Inch All-in-One Desktop
see here: http://www.amazon.com/...00KRA648U/
or
MSI G Series AG220 2PE-005US 21.5-Inch All-in-One Touchscreen Desktop
see here: http://www.amazon.com/...00KRA5X8C/
Those are two excellent gamers. Arguable the best two all in one PCs under $1500.
The far surpass your requirements.
Both of these computers have;
Intel Core i7-4700HQ 2.4 GHz (6 MB Cache) Quad core processor
12 GB RAM
1 TB 7200 rpm Hard Drive
NVIDIA GeForce GTX860M Graphics with 2GB GDDR5 VRAM
Windows 8.1
Asus is also a very reliable brand and brand that has a really positive reputation in the computer industry.
Now, the difference between those two PCs that causes the difference in price is the fact that the MSI G Series AG220 2PE-005US PC has an additional 128 GB Solid-State Drive TO ITS PRIMARY 1000 gb Hard drive. An SSD gives your PC additional storage as well as more speed.
Make your choice.
Either way you take it, you will be getting a superb machine