He would not be prosecuted under our law, he would not be extradited to the UK to serve an English sentence within the confines of our law. Furthermore he would not do an English sentence in an American prison, so to speak.

Think about how long murderers and rapists serve in our country and then weigh the severity against slander.

The cross-country element of this could make it tricky, perhaps you could bring charges upon him based on my previous advice of seeking legal counsel HOWEVER a success for you would be to report the video and get it taken down.

You could not on the strength of this one video get his channel taken down however if you can find numerous occurrences the strikes would stack up and his channel would be terminated.

One thing that could help, do you make money from Youtube? It doesn't matter if it's a penny, you could argue that his accusations, as of course they defame you, also defame you professionally and directly hinder you from making money, that will be a very good trick up your sleeve.

As for recording your voice, you do not have a leg to stand on, he didn't stick a microphone through your window, you were not in a personal space per se, but a cyber-space, and were allowing your voice to be heard by whomever could have recorded it. If it does not fall under any wire tap laws and he did not unlawfully access an audio recording of your voice or unlawfully create an audio recording of your voice then I wouldn't waste your time pursuing that avenue.

Definitely gather your ammo, you will need ammo, I also think that because this is seemingly petty to some (as it's to do with video games), a legal professional may not take this seriously, at least not the first one you contact, but who knows?

The long and short of it is nobody should be allowed to outright call someone a paedophile on the internet and get away with it, it's not even text, which you could NOT prove was sent by him, it's his VOICE so download the video in case he removes it.