'Watch it work' is not a special phrase. Verbs such as see, hear, notice, watch, etc can be followed by a direct object and a bare infinitive or an ing form: I saw him cross/crossing the road . He crossed/was crossing the road, and the speaker saw this.
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AnonymousAt first I thought it was an object complement, then a verbal reduction, but both do not work.I turned on my new Roomba and watched it work.