Are mitochondria dead?
SolarLunix posted an excellent answer detailing the criteria for being classified as "alive", and showed that by those criteria, mitochondria could be considered as "dead".

However, I would argue that the narrator's statement in your video does not make any sense. The currently-accepted theory of the evolution of mitochondria (and possibly other organelles) from free-living prokaryotes is called symbiogenesis and postulates that the mitochondrial progenitors began living symbiotically with the precursors to eukaryotes some 1.5 billion years ago. Life originated on Earth about 3.5 billion years ago, so eukaryotic cells (carrying mitochondria) have been around for a little less than half of that time.

In that incredibly large span of time (if you counted 1 number per second, you'd reach 1.5 billion in about 47.5 years), what used to be an independent organism (we assume) has become an organelle - an integral part of the eukaryotic cell. It absolutely could not survive outside the cell on its own, and relies on signals from the cell (mainly, the cell's energy needs as detected by "sensor" proteins to key molecules like glucose and ATP) to reproduce.

Therefore, it is most appropriate to think of mitochondria simply as another organelle, just like the endoplasmic reticulum, lysosomes, or the nucleus. It doesn't make sense to think of those other structures as "alive" or "dead", just as it doesn't make sense to think of mitochondria in the same way. Yes, they used to be independent, but are no longer; instead they are a well-integrated part of the whole cell.