Cooking an ultra modern kitchen was the aspiration of postwar housewives, and this short appeals to that audience. Olive's kitchen has all the very latest appliances and accessories. Checkerboard style cakes (often dusted with coconut on the vanilla squares) were a popular cake fad at the time.
The nephews here belong to Olive in this short. Usually, they are from Popeye's family. As ever, there's no mention of either character's siblings. Giving cartoon characters nieces and nephews was a clever way of showing their parental skills without the production code requirements of a wedding back then.