Oh god, that video again.
Every single information you got out of that video is nonsense. Complete bullshit, far from reality.
That said, an I7 3770k/4770k and especially 4790k demolish the 8350 fx in everything, especially gaming.
I7 4790k is currently the best cpu for gaming, if you don't overclock. But that's just due to it's high base clock speeds with the most modern architecture.
So, the I7 4790k won't limit any gaming performance. It's strong enough to support any dual gpu setup there is. Even two 980 gtx's overclocked to their limits or two r9 295x2's.
And what goes for gaming, is true for streaming too. In fact, I don't even see any fps difference between just gaming or gaming and streaming.
It's just nothing that would even get that cpu to sweat.
And once more about teksyndicate: Disregard that channel. I have not decided weather I should believe he's paid by amd, or just suffers mental issues, but his whole channel is mainly a compilation of bullshit information wildly (and randomly) scramled into his videos.
But actually, as you do not care about rendering, you won't see much (if any) difference between an I5 and an I7. For real time workloads (such as gaming), they're just about equal. Especially when you have a new gpu (r9 series/gtx 600/700/900 series) to take advantage of hardware encoding.
The most quality limiting factor (on the website where it is to be displayed) is your, or the video stream hosters internet connection. Usually the streamers, tho.
To finally answer your question, in a scenario where you have unlimited gpu power (I.e. three 980's) an I5 4690k at stock (3.7ghz turbo all cores) would perform about 30% better than a 8350 fx on 5ghz. In gaming, the I5 on 2.8ghz is equal to the fx at 5ghz. The I7 would give about the same, just about 1-2% better than the I5 on same clock speed.
Now, you wanted numbers. It's impossible to give those without knowing your gpu(s) and the games you intend to play (=stream).
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