very nice video indeed!
as for the cost, professional turnkey solutions are in excess of 15.000 eur (which is still relatively cheap compared to full-scale helis, but not quite as fast-going) but amateur kits can be built for no more than 400 eur.
Camera payload and stabilization (via advanced gimbals) are the biggest challenges and designing a drone capable of following a WRC car at 200 km/h would require really large structures, and electrical power storage is still difficult, so runtimes are usually low (10-15 min).
The hobbyist term is "multicopter", you can read a lot on forums such as rcgroups, it's really interesting.