Does the definition of the word “Jew” mean that you have to believe in G-d, or you can follow the historic tradition?
Being a Jew does imply belief in G-d. Although a Jew who doesn’t believe in G-d doesn’t stop being a Jew, he does stop doing the most basic thing that a Jew does, and according to Rambam (Commentary to Mishnah, Sanhedrin chap. 10) he actually loses the name Israel. Although Judaism (unlike christianity) is a very practical religion, involving a great number of laws and ordinances, religious practice without belief in G-d is devoid of all meaning. The deeds of a Jew are dedicated to the service of G-d, and one who doesn’t believe in G-d therefore doesn’t believe in his own deeds, or his own basic purpose in life. The Gemara (Makkos 24) therefore states that if we wish to express all of the mitzvos of the Torah in one, single concept, that concept would be faith in G-d: “A righteous person lives by his faith.”