It really isn't that far behind but it is behind.
Like I said I have and use an 8350 running at 4 GHz for PC gaming and emulation and it does the job quite well. PC gaming is also quite different than emulation because of how emulation actually works and utilizes the CPU. Emulation in the vast majority of cases only uses a single core of a processor and in a couple of cases such as the Dolphin emulator uses 2 and single core performance is most important factor when it comes to emulation speed. As far as I am aware of right now only the PS3 emulator, RPCS3 uses multiple cores effectively because the PS3 itself uses multiple core CPUs.
You can overcome some single performance with raw clock speed so for example a 4GHz AMD CPU can perform equally as well as a 3.2 GHz (approx) Intel CPU but if you got equal or very close to equal clock speeds the Intel will perform better. Also keep in mind that with these levels of CPUs you will only see any real issues on the most modern of emulators such as Cemu and RPCS3. Both of those emulators are still in their infancy relatively speaking regardless of any videos showing off a few hand selected games.
I have not bothered trying out the RPCS3 emulator just because I have zero interest in it but I have toyed around with Cemu a bit and my 8350 does the jobs and runs most of the games at full speed, Breath of the Wild is the one game I threw at it and does not run at full speed at all on my system. PS2 emulation with PCSX2 and Saturn emulation with Mednafen the 8350 has no problems with them.
The bottom line is this. For the mature emulators out there a relatively modern AMD CPU running at or close to 4 GHz will perform perfectly fine. You will only find more benefit with an Intel CPU when it comes to the more cutting edge newer emulators such as Cemu and RPCS3.
If you were to be buying a new system and emulation is something you intend on using it for quite a lot and want the best performance definitely buy an Intel based system. That is what I will be doing next year when I build my next system. But if you want to save a few bucks and focus on more the PC side with emulation up to and including PS2, Wii and maybe a dash of Wii U then something like a Ryzen is a great choice.