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.