I'm not as familiar with streaming and there are a lot of variables that impact performance. It depends if someone's using twitch, obs, xsplit, making use of nvidia's nvenc encoding and so on. While it sounds simple, streaming is a rather broad topic much like gaming is. Gaming can include anything from minecraft to witcher 3.
For heavier multitasking at the same price as your original build, there are i7 systems which will likely beat out both the i5 and 8350 in gaming/streaming.
http://www.amazon.co.uk/4x3-6GHz-Windows-wireless-cardreader-multimedia/dp/B00SHK949S/ref=pd_sim_sbs_147_21?ie=UTF8&refRID=0D7MXKB2ST12AV5TRYHG
Most games don't need 8 cores/threads. The 8350's advantage may be when streaming which again really depends on what resolution, software, if gpu encoding is used or not etc. Even if it streams smooth, the cores themselves are weaker meaning less performance in games. The i7 has twice as many threads as the i5 and the only reason it's often passed up is because of price. For whatever reason, these systems have the i7 priced the same as the 8350 which takes away any price advantage amd may have had.
It did say it included the gtx 750 where the previous systems had the 960 so the graphics card isn't quite as strong. Though for newer games a better card than either would probably be desirable. These are budget prebuilt gaming rigs. From the two games mentioned, I believe both are heavy on the cpu and use little in the way of gpu so this would be a non issue. Finding benchmarks for older games with newer hardware isn't always easy. Most civ v benchmarks are from 2010/2011 with much older gpu's, newer benchmarks revolve around civilization beyond earth. At least from what I could find.