Why isn't Hanukkah a religious holiday?

It is a religious holiday. However it is not a holiday prescribed by the Torah, but was added at a later time by the Rabbis as a celebration of the miracle of the jug of oil. Therefore we are not forbidden from performing any acts of creation, as we are on the Sabbath or holidays that come from the Torah.

Purim is another holiday prescribed by the sages (the last of the prophets), and therefore is also not a Holy day.