Royer Oscillator is also known as a self saturating oscillator.
The transformer is a push-pull type. When one side saturates, it turns off and the other side turns on.
The oscillation frequency depends on the L of the coil and the C of the capacitor, and the stray LC and parasitic LC.
You need a core material that will support successive saturation at a reasonable frequency.
You do not want matched transistors, as it is the minor differences that get the thing started. Same type yes, but not matched.
There are several good sources on this on the internet.
As a side issue, the X-Ray video is very pretty, but I have concerns about Murat Erie's intellectual property and the propriety of X-raying it.