Here’s a couple of examples of curved and twisting takeoffs:
youtube.com/watch?v=67M-aRlY4ZM
youtube.com/watch?v=R48L3_PPVrs
Never happen in the US. The NTSB and the FAA already think most pilots can’t maneuver their airplanes ( pt121 ops usually prohibit circling approaches). Check the last SAFO issued by the FAA on visual approaches. This airport configuration would drive the NTSB absolutely nuts!
“best of the web” this is not.
A silly old idea rehashed by sensationalized press for clicks it is.
A lot of that (old) concept is contradictory. If you really want to use it with 3 A/C at once, that will not mix with the promise to “take-off and land in any direction” as that will require every airplane to use a specific position (unless you match departures going in three different directions which is pretty unlikely to work out even at a large airport). While the banked runway would eliminate skidding, a banked airplane will have less lift at a time it is needed most. The incline/tilt required is dependent on speed, car speedways often have increasing tilt towards the outside. That won’t work for aircraft due to wingtip clearance requirements. Another unsolved problem would be that where you exit that circle on departure depends a lot on your weight, so would you start your take-off roll to leave at a pre-determined exit point or rather have a larger possible exit area? You’d need a lot of obstacle clearance all around to ensure that engine-out departures have a uniform obstacle clear surface from which to proceed (where?).