Ughh, this is an iOS bug with workarounds being posted on YouTube dating back 16 months.
Apparently the mic is a different audio track from any internal audio playing from the phone. You end up with two audio tracks in the video and the default is the internal audio track. So when you upload that video to YouTube, another website or try to play it in a player like VLC, you don't hear the mic recorded audio.
Two options I've seen are to either play the video back on your phone, whilst screen recording the original recording. This will record a duplicate of the video but capture the original mic audio onto the internal audio track, so the second video will work anywhere.
The other option is to use handbrake to re-encode using second audio track. But I think that means you'll lose any internal audio if you had a mix or internal and voiceover.
Seems like a big issue with the iOS screen recorder. It's a widespread issue for iOS gamers who like to record and share their footage.
I'm not sure if there's any kind of official Apple big report though. I'll ping them a feedback message.