A Jew is any person whose mother was a Jew or any person who has gone through the formal process of conversion to Judaism (See
Judaism 101: Who Is a Jew?). The reason why orthodox Jews view themselves this way is because of God's ancient old covenant relationship with the nation state of Israel.
Though God blessed Ishmael and said he would become a "great nation," God never had a covenant relationship with a nation state deriving from Ishmael. Islam wasn't even fabricated until the sixth century AD. Islam is NOT a race. It is a false religious system.