Although the video concentrates on quantum entanglement, it's fairly uncontroversial that relativity suggests this, not least because the whole notion of a single moment in time becomes relative in special relativity and arbitrary in general relativity.
For example, using only special relativity and ignoring the motion of the earth, if two people walk past each other at a relative speed of about 4 mph, then what is happening simultaneously to that event, at the distance of the Andromeda galaxy, differs between the two observers by about five and a half days. What's in the future to one of them has already happened according to the other.
In the case of general relativity, if we take an extreme example like a black hole and define space and time in a way that makes sense at a large distance from it, they break down completely at the event horizon, when, relative to the distant observer, the notions of space and time swap over entirely (the distance to the centre becomes timelike and the time coordinate becomes spacelike).
"People like us who believe in physics know that the distinction between past, present and future is only a stubbornly persistent illusion." -- Albert Einstein.