If you get a complaint(s) YouTube will probably force you to change out the audio on your videos which will destroy the premise.
But he's using music tracks that YouTube offers, right? The only problem with this method is that you can not earn money from such videos - all the profit from the ad's goes to music owners.
By the way, from Germany this link is not available at all, because "GEMA has not granted the respective music rights". Funny, huh? Instead of just blocking the sound and showing silent video they block the whole video.
I didn't check but I think it doesn't matter. I'm pretty sure for whatever reason, you can't play a song over speakers and record it, you must use the YouTube audio replacement feature. I don't know how much this is YouTube policy versus various copyright laws in the countries involved.
For example, in the US even if you own an audio CD, you can't play the CD over speakers in a business or as part of a public performance without a license for commercial use.
There are many example of truly absurd lawsuits and claims around performances of copyrighted works. One particularly egregious example is that the American Society of Composers, Authors & Publishers demanded royalties from the Girl Scouts of America for singing campfire songs.
When it comes to copyright law, and especially music copyrights, even if the law is on your side you'll likely be strong-armed into a defeat long before you're able to have your days, months, and years in court.