And this rule regarding intermediaries applies even if it's due do the same wetness correct?

So another person touches najes leather that is wet due to rain, his hand becomes 1st motanajjes, then he touches the door knob few seconds later, it becomes the 2nd. Then I come and touch it which makes my hand the 3rd, now it can't make anything else najes. Or should the other person's hand first dry, and then be exposed to new wetness for the door knob to become the 2nd mutanajjis?

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It doesn’t have to be dry, unless the actual Najasa is there. For example, if one’s hand touches urine, then his hand touches the doorknob and drops of urine are transferred to the doorknob, then in this case the Najasa itself is present on the doorknob. Urine is considered Ayn al-Najasa, so the “intermediary” discussion doesn’t apply to the doorknob when the Najasa is present. Yes, if the actual urine wasn’t present, then the discussion on intermediaries applies.