It's not circular.
Theism applies to gods, while gods do not derive their definition from the word theism. Gods have a variety of definitions. Here are some:
noun 1. the one Supreme Being, the creator and ruler of the universe.
2. the Supreme Being considered with reference to a particular attribute: the God of Islam.
3. ( lowercase
) one of several deities, esp. a male deity, presiding over some portion of worldly affairs.
4. ( often lowercase
) a supreme being according to some particular conception: the god of mercy.
5. Christian Science . the Supreme Being, understood as Life, Truth,
love, Mind, Soul, Spirit, Principle.
6. ( lowercase
) an image of a deity; an idol.
7. ( lowercase
) any deified person or object.
8. ( often lowercase
) Gods, Theater . a. the upper balcony in a theater.
b. the spectators in this part of the balcony.
The first four definitions are particularly relevant here.