I think we can all agree that Gandalf is a meddling jackass who always gets things wrong Not really though he is not infallible like all of the Wise. It is possible that he said "kings" just to make it simpler, instead of "Lords and Kings".
One thing that might weaken the argument is actually in the verse about the rings itself, look at line three on the Nazgul, it doesn't say anything about them being kings, though the quote you have from the Sil points to at least two (could even just be the WK). Interestingly the verse also throws doubt on the actual wording, the elven rings were only worn by two kings, Gil-Gilad and Celebrimbor though Gil-Gilad wore two of them before handing them onto others (Círdan and Elrond) and Celebrimbor gave his to Galadriel.
''Three Rings for the Elven-kings under the sky,
Seven for the Dwarf-lords in their halls of stone,
Nine for Mortal Men doomed to die,
One for the Dark Lord on his dark throne
In the Land of Mordor where the Shadows lie.
One Ring to rule them all, One Ring to find them,
One Ring to bring them all and in the darkness bind them
In the Land of Mordor where the Shadows lie."