But nobody is "constantly tracking and publishing his whereabouts".
The information published is not constant: it is published only when a plane takes off or lands.
The information is not a person's whereabouts - it is that of a vehicle
It could be argued that taking a flight in a private jet is just as much an example of what you term a public event as being at a sports event is, since private jets are required by law to broadcast their exact id and location whenever they are in flight.
The GDPR only applies to businesses, not individuals. So, clearly in this case it does not apply at all since the person behind @ElonJet is acting in an individual capacity.