Here's my theory: they aren't concerned with the movies and TV shows shown in the video (which are presumably obtained legally as Jeff mentioned), but rather the brief use of what looks like [plugin.video.youtube] (https://github.com/anxdpanic/plugin.video.youtube) at about 12:10 in the video.
The plugin is an alternate frontend to YouTube, and as such, allows bypassing ads. He never mentions the plugin explicitly in the video, but I'm pretty sure that's what it is; he mentions YouTube and is clearly watching one of his own YT videos in Kodi. Just today, I noticed YouTube getting more aggressive in its anti-ad-blocking measures. They got really strict a year or two ago, backed off a bit, and seem to have ramped up again. My guess is that someone in management needs to show better numbers and is looking for ways to punish anyone even hinting at accessing YouTube without the obligatory dose of advertising.