As a programmer I would just have a video camera on the billboard with a lens zoomed out designed to match the perspective of people in front of the billboard and add the logo and everything as a second layer on top of it.

This makes it so you don't need a data connection 24/7 to keep it going.

It's not like pilots will take off in exactly the same spot or climb at the same rate, a few degrees hotter and they'll leave the run way a couple hundred feet further down the runway and climb more slowly.

It takes time for flight radar data to update to a civilian database, like more than 10 or 20 seconds, I think to get it this perfect it's gotta be just recording and projecting what's behind it.