According to the article, particles 1 and 4 do not coexist. Therefore, one must be destroyed before the other is created.
But if 1 is destroyed before 4 is created, then the entanglement of 1 and 2 is broken before 3 and 4 are created (because 3 and 4 are created together, and then 2 and 3 are entangled).
So, by the time 2 and 3 are entangled, 1 does not exist, because 3 already exists and is entangled with 4.
The question that arises is then how do they know that 1 and 4 are entangled?
It could simply be that 1 and 4 show the same state when measured, because 1 and 2 were entangled, then 3 and 4, then 2 and 3. Which means that whatever entanglement existed between 1 and 2 will exist between 1 and 3 and 1 and 4, even if 1 does not exist.
That does not mean particles are entangled across time. It may mean that entaglement is simply peristent and transmiitable.
Most probably there is a misunderstanding somewhere between the announcement and the article, so please anyone that knows more, elaborate.