It's even worse than just the same flight number. Both were at PHX, one landing, one taking off at the same time. Kudos to a clever ATC for preventing what could've been a catastrophe: https://youtu.be/93lLXNsWp9Q
The probability of it becoming a catastrophe was infinitesimally low with the existence of TCAS.
The YouTube video you link to is actually about a separate incident from the one described in the article. The video is about an incident involving two AAL2482s near Phoenix; the article is about an incident involving two AA5083s near Providence.
It's the same idea though; one was inbound, the other outbound, and ATC had to distinguish between the two.
[edit: Corrected locations.]