However, I was under the impression that the old nobility of Japan was done away with after WWII?

Correct. Part of the terms of the 1946 constitution was that the only hereditary titles that would be retained in Japan were for the imperial family. Any member of the Kazoku lost their title as a result, although many understandably were able to utilize existing wealth, assets and influence to remain fairly important in Post-war Japan. This also applied to the Shinnoke or cadet wings of the royal family.

I was reading recently about a princess of the Japanese Imperial House who would have to renounce her status and title because she was marrying outside the nobility.

So surely anyone she chooses to marry is a 'commoner'. Or are the old noble houses still considered to be nobility in all but official title?

You have to remember that in Japan, royal lineage follows the men of the royal family. Laws and traditions have changed- Empress Michiko was the first commoner to marry into the royal family- but you do have a firm grasp on it. Unless she marries within the family, a woman in the royal family cannot retain her status as a married woman. Although there is some back and forth as to whether this was the product of an oversight with the Japanese government hastily slapping together constitutional laws to keep in accordance with their new constitution while also keeping the royal family's size to a minimum, the broader context of laws concerning the Royal Family of Japan tends to be, "we will cross that bridge when we get to it."

It's a purely modern example, but after the recent succession crisis in 2005, when it was rapidly becoming clear that there would be no male heir to ascend to the throne as the current emperor aged, the major push for academics, lawyers, politicians and other legal experts to consult established laws and find some way of maintaining the family line- in this case, by amending it to allow a woman to be first in line for the throne- it all was put on the back burner once a male heir was produced.