Is this a good gaming/live streaming computer?!?

Yes - it's a good computer. I would contact them asking them if they could exchange the processor for an intel i5-3570k as it performs better and costs less. Of course, they'll charge you, but I have to admit you found one of the better prebuilts.

Although, I do highly recommend building it yourself as you could save $100+

Don't bother with the Liquid Cooling, as it's unspecified, which means it's probably junk compared to a Hyper 212.

Get a 990FX instead of the 970 if you're going that premium.

Get an SSD.

Or better yet, if you're spending 1100, get an i5.

Intel CPUs are better than AMD, no explanation necessary.

do you already have a monitor, keyboard and mouse, thermal paste, operating system, wifi or usb wireless adapter for wireless internet connection, computer case, and cd rom? because you didnt mention those.

actually none of this will help unless you have internet speeds above 16 mbps!