Early Installment Weirdness; GRRM hadn’t keyed in yet on the whole idea that Kingsguard don’t inherit.
I mean, technically Wardenships aren’t lands but royal offices, and if Kingsguard can be Hands, then there’s no reason they can’t be Wardens too. However, it’s clear from context that GRRM was thinking of Jaime as Tywin’s heir in Eddard II.