I miss the music, but I don't think he could keep putting it in as more and more people started watching. There are people who really don't want their songs used in any context without their permission, even when it might technically be permissible under Fair Use, Parody or other exemptions, when it makes money. If they think they can gain money by suing, they will.
If, on the other hand, they thought that the videos were actually promoting music they were having a problem selling anyway, they would probably let it keep going, and just refrain from prosecution because it would serve as free marketing.
Hypocritical? Yes. But good business practice.
So, in short, while I think the artistic merits are there, I don't think having Yahtzee sued would help Zero Punctuation. Better to have most of what you want, rather than none at all.