My understanding is that the person who originally called criticism of the Israel gov 'antisemitism' is the one equating Jewish people with the state of Israel

That's the point they are making actually, that Jewish people that call for antisemitism in those cases like the Australian Jewish organization and tons of Israel supporters, by saying that being against genocide is antisemitic, they are saying that genocide is semitic, which is a very dangerous statement.

In my opinion, those that make such ludicrous statement are the antisemitic ones, for calling the Jewish religious group genocidal.

Clearly the Australian Jewish Association is relating Jewish people to genocide, otherwise they would not have called that statement by a shopkeeper in New Zeeland anti-semitic but would instead have said it to be anti-Israel.

They're directly saying that being against this Genocide is being against Jews, which is most definitelly "relating Jewish people to that Genocide"