There are many distinctions to be made.
Many states have ceased to recognize Assad's regime as the sole legitimate government of Syria.
Assad's regime did not have effective control of large swaths of Syria.
It isn't clear if the question contemplates Russian intervention at the invitation of Assad's regime as part of "Western states' actions in Syria".
The U.S. involvement was pursuant to a de facto declaration of war passed by Congress (the Authorization for Use of Military Force (2001) that also authorized intervention in Afghanistan's civil war). Many other intervening states similarly authorized action, at least, against ISIS.
Turkey's involvement is justified by a shared border and the risk of military attack from the Syrian side of the border not effectively controlled by the Assad regime, a situation not present in Nicaragua v. United States.
U.N. Security Council resolutions address some of the actions.
Some of the Western actions in Syria were authorized by international treaties relating to the use of chemical weapons.
Finally, it bears stating that rulings of the International Court of Justice (ICJ) are basically unenforceable unless all parties to the litigation there agree to honor its rulings and even then, its rulings are generally only enforceable in the domestic courts of the parties. The U.S. has a long standing practice of not really respecting ICJ rulings faithfully, and of certainly not treating them as obligatory.
The U.S. did not formally defend itself in or participate in the proceedings in Nicaragua v. United States because it took the position that the Court had no jurisdiction over it, and the U.S. has not honored that ruling.