Reading about the Tectonic Evolution of the Levant Basin. Pre-dosing with Tylenol is recommended.
The important take away is there really exists such things as rifts, fracture, and folds. Whether it's the African, or Arabian plate, they are not homologous geological structures for a given plate. And that is why oil can be found in the Eastern Med, or in KSA, without being present in Israel onshore in economical amounts.
A drill down on the graphic in the link you posted shows Israel and Lebanon are on the African "Plate".
So there is no inference to be made that Israel has onshore oil just because it's neighbors do.
As to rivers changing direction, I don't see a link between the Leviathan gas deposits and the Chicago Ship and San Canal.
And so far as rivers meandering it's fascinating to fly over the lower Mississippi, because the effect is so obvious when looking down. There's oil and gas off the coast in the Gulf of Mexico for the exact same reason there is in the Eastern Mediterranean.