Not all Semites are Jews.
The phrase "anti Semitism" came into common use in the late 1800's / early 1900's as a way of saying "anti Jewish" in the developed world without being seen as too racist. It is an actual dog-whistle.
Doesn’t matter. The dictionary definition of antisemitism is an animus towards Jewish people.
Antisemitism was a “polite” way to say Jew hatred. It was a euphemism.
Arabs and etc were not included in the “semitic”, for the original reasons of the coinage, as at the time few were bothered by them and they had no political-social significance.
These days we can call it obsolete, but there is no replacement as yet.