This is taken from the current Online Oxford Dictionary:
theism
[ˈθiːɪz(ə)m]
NOUN
belief in the existence of a god or gods, specifically of a creator who intervenes in the universe.Compare with deism.
"there are many different forms of theism".
Link please, because that isn't what I see on the online Oxford English Dictionary (which is a sign-in). This is what I get:
theism, n.1
Etymology: modern < Greek θεός god + -ism suffix. Compare French théisme (Voltaire).
(a) gen. Belief in a deity, or deities, as opposed to atheism. (b) Belief in one god, as opposed to polytheism or pantheism; = monotheism n. (c) Belief in the existence of God, with denial of revelation: = deism n. (d) esp. Belief in one God as creator and supreme ruler of the universe, without denial of revelation: in this use distinguished from deism.
So the general definition is as I've described - believe in god (described in this definition as deities) - there are some narrower definitions, one of which is about monotheism. A further one is clear that deism can be considered to be theism, and final a more limited definition that distinguishes theism from deism and from the general definition - again using especially, not specifically or exclusively.
You seem to be focusing only on (d) which is no more relevant than (c) but definitely less relevant than the general definition.