What functional groups are subsets of the Alkoxy group?

Question

In a quiz, I was asked to find all of the combinations of organic molecule of $\ce{C4H6O2}$. The combination excludes -COOH, -OH, double bonds and the alkoxy group.

The only problem, as far as I am concerned, is the definition of the term "alkoxy group". According to this Wikipedia article, a Peroxy or Methelenedioxy should be one of the possible combinations allowed. However, the names do have the "-oxy" suffix in them. So I am uncertain whether to include Peroxy's and Methelenedioxy's in the list.

P.S. Below is a picture of the Methelenedioxy group and the peroxy group, respectively, from the already mentioned Wikipedia article.

Answer 1

There is another Wkipedia article entitled "Alkoxy group". In it they show the following molecules as containing alkoxy groups.

They include methylenedioxy, but not peroxide in their list.

Answer 2

Alkoxy groups are ethers, so I would consider methylenedioxy as a subset of alkoxy groups (although the reactivity is pretty different).

Peroxy is not an ether, so I would consider it distinct from an alkoxy group.

Given those functional group restrictions, it seems like the quiz was trying to force you into a particular line of thinking. Without alcohols and ethers, I think the only thing left would be peroxides, but perhaps I'm missing something.