How do you know that someone doesn't implicitly believe in one of them then?
You aren't going to implicitly believe in Woden, but you can in theory implicitly believe in something that meets the description of some form of god without being consciously aware of it.
Whose description?
Not yours - other people can have different views on what constitutes a god.
Not some objective definition of "god"; there isn't one.
The only view that matters when deciding if the person is a theist is the person's own view. If they have formed a concept of god and believe in at least one thing that meets it, then the person is an explicit theist. If a person has no concept of god, then they can't be a theist at all, implicit or explicit. You can't believe in sonething you haven't conceived.
Maybe someone gives them an explanation of the god they believe in and the 'implicit theist' says 'Yes, that's what I have always believed too!'
If one person convinces another to adopt a particular definition of "god" that matches up with something they already believe, that's the moment when they become a theist.
Does a child love its mother before it learns the word love? They implicitly love their mother without being aware of the terminology.
We don't base judgements of love on the understanding of the person doing the loving. We do base judgements of theism on the understanding of the person doing the believing. This is why a Christian can still be a monotheist even though he believes in an entity (the divine messenger Gabriel) that is almost identical in any relevant respect to an entity that another religion considers a god (the divine messenger Mercury): only the Christian's understanding is what makes the difference between monotheism and polytheism.
... BTW: what sort of theists are these "implicit theists"? Are they monotheists? Polytheists? Pantheists?
I'm not advocating using the expression implicit theist, but if some people are going to use implicit atheist then it is worth pointing out that there remains at least a possibility that some of these 'implicit atheists' may meet the definition of being an implicit theist.
An implicit atheist is someone who doesn't have any belief in gods because he hasn't given thought to the question of gods.
Using the same formulation, an implicit theist would be someone who has belief in a god or gods because he hasn't given thought to the question of gods.
... but to be a theist, one must have a concept of god, which means he must have given thought to the question of gods.
As sceptics, should we not reserve judgement on such people rather than jumping to some conclusion without any evidence?
As skeptics, shouldn't we reject concepts that are inherently contradictory?