I'm embarassed to say I actually googled it and came up with
this:
Designed to counter high-speed, high-altitude
anti-ship cruise missiles.
Underpaid, it's a joke. If it has to be a cruiser, then
technically carriers qualify under the Russian definition.
Anyway, if we consider the Burke class then we have to bring in
the KDX-III, which has 16 fewer Mk41 cells but 32 more K-VLS cells
for cruise missiles and VLS ASROC (meaning an overall 16 more Mk41
cells available for air defence, ie potentially 64 more ESSMs).
It even has a RAM launcher for point defence, but that shouldn't
count towards it being an "air defence ship".