Original title is 猫タワーの戦い. 猫タワー is "nekotawaa" so タワー is a loanword from the English word "tower" obviously. And yes, it refers to the piece of furniture for cats to climb, scratch and sit on.

August 31st, 2011. Author's note:
"Q: Please tell us where your power spot is.
A: The futon."