I don't know if the pictures that show the terminal are indicative of the peak water level, but if so then it's just possible that the terminal has got away with it. Most of the public areas are upstairs, apart from the baggage / arrivals hall.
The entire terminal building is supported on hydraulic jacks, used to keep it level as the artificial island settles underneath it. I think there's a ton of machinery for all that in a basement level below, and that'll all be wrecked. Fortunately the hydraulics are only required to change the level (steel shims are inserted after a lift), so it can probably all be replaced. KIX is an expensive airport to run, and it's just got pricier. They may need a bail out from the local prefectural government, and taller sea walls.
The eastern side of the airport is the main terminal where the likes of Lufthansa, Cathay, etc fly to. The other side is where Peach Aviation operates from, and they've probably got away with it over there.
The bridge has taken a proper walloping - a lot is going to depend on whether that displaced section has also dislodged the adjacent railway section and the road section on the other side, or moved the bridge pier. If they're unserviceable, that's going to take ages to fix. I worry that if that's the case then the likes of LH and KLM might use it as an excuse to stop services to KIX altogether, which would be annoying.
TBH the bridge could do with a significant upgrade - I've nearly missed flights before from KIX due to the trains being stopped due strong winds (the aftermath of a typhoon).
EDIT - just seen some other video, looks like the ground floor of the terminal has got soggy, but only just.