The footage was recently obtained by the USCG and shows Wendy Rush, the wife of Mr Rush, hearing the sound of the implosion while watching on from the sub's support ship and asking: "What was that bang?"
The video has been presented as evidence to the USCG Marine Board of Investigation, which has spent the last two years looking into the sub's catastrophic failure.
The documentary also reveals the carbon fibre used to build the submersible started to break apart a year before the fatal dive.
Titan's support ship was with the sub while it was diving in the Atlantic Ocean. The video shows Mrs Rush, who was a director of Oceangate with her husband, sitting in front of a computer that was used to send and receive text messages from Titan.
When the sub reaches a depth of about 3,300m, a noise that sounds like a door slamming is heard. Mrs Rush is seen to pause then look up and ask other Oceangate crew members what the noise was.
Within moments she then receives a text message from the sub saying it had dropped two weights, which seems to have led her to mistakenly think the dive was proceeding as expected.
The USCG says the noise was in fact the sound of Titan imploding. However, the text message, which must have been sent just before the sub failed, took longer to reach the ship than the sound of the implosion.
All five people on board Titan died instantly.