That's the earliest alphabetic writing system. The Sumerian writing system started out pictographic (like hieroglyphs), and predates that Syrian find by about 800 years.

It became less pictographic over time, and that Syrian site is only 500 miles from the Sumerian empire. My amateur speculation would be that trade with Sumer brought writing to Syria and they developed the idea in a different direction, arriving at this alphabetic system.

that was about the oldest alphabet, not writing system