What a broadcast is and what isn't is a pretty interesting legal debate actually, mostly because these rules were made way before the internet. And also because every country defines broadcast a bit different. However, all of these definitions have in common that on demand playback doesn't count as broadcast, so your youtube video is good to go.

It becomes a different matter altogether when we are talking about live streaming, eg. via youtube live streaming. In Germany for example that would count as broadcasting, which is why youtube doesn't allow Germans to consume or produce live streams.