Using the pronoun "one" is simply the speaker's recognition that it is, in fact, two watches that he is asking about, but without repeating the word watch . Which is your watch, this [one / watch] or that [one / watch]? Without "one", it seems that the speaker has failed to recognize what he is asking about, as if there were a puppy in one basket and a kitten in another and asking Which is your watch, this or that?
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