Odd. Just to check, I went to the playground page you linked in your first post, scrolled to the bottom and followed this link:
https://code.google.com/p/arduino-hih61xx
Then I clicked on the Downloads tab and downloaded HIH-0.2.tar.gz. When extracted, this had two library folders: HIH61XX and HIH61XXCommander. Did you get your library from a different place?
Do you have an example program for the library showing up in the Arduino IDE (under File - Examples)? If so, does it compile?
EDIT: Can you confirm the path and folder where you installed the HIH61XX files (.h and .cpp)?
Cheers
Ray