Irish: a stream, a current — water that carries by flowing. In modern Irish the same root carries live media: sruthú, streaming.
Irish sruth (a stream, a current), from Old Irish sruth, from Proto-Celtic *srutos; the modern derivative sruthú (streaming) carries the same current into digital media.
Water that carries by flowing, and now the media that arrives the same way, continuous rather than delivered all at once. The old word for a current is exact for what streaming actually does.