From Waite’s comment on the Emperor in the PKT:
“He is the virile power, to which the Empress responds. . .”
and
“The Emperor has been described as (a) will in its embodied form, but this is only one of its applications. . .”
Will corresponds to fire, so the fact that the Kings are seated doesn’t prevent them from being in agreement with fire. The Emperor is also seated.
I don’t think Waite’s confused here. For him the Kings are Chokmah and Yod; the connection with fire is Will.
Whether the Emperor is seated has nothing to do with his Fire attribution. He is Aries, Cardinal Fire. Likewise, whether or not a court is seated has nothing whatsoever to do with the element. It is just a way of distinguishing between Knights (horseback) and Kings (seated in chariots or on thrones).
If we are to assign masculine elements, Fire and Air, to the masculine court cards, the Knights seem more spirited (Fire), and the Kings more cerebral (Air), the other option doesn't fit as well, it seems to me.
Anyhow, if, as Kwaw contends, Waite is using GD terminology, then the horse riders are Yod and Chokmah, and the charioteers are Vau and the Microprosopus, and the elemental attributions follow from this.