Dry rot?

Doesn't look like it, but it's difficult to see the photo. The rusty grate there seems to indicate excessive moisture in the corner, and that could contribute to the wood rot.

Termite damage usually looks like little tunnels parallel to the grain of the wood. Sometimes you'll see brown mud tubes on the surface of the wood.

Did the inspector say that it was termites? Also - is that rust on the metal register grill on the right?

Thats WATER infiltration. Likely incorrect flashing.

Yes looks like rust. What do you think happened to cause water infiltration?