The most important property that separates a macro lens from others is its maximum magnification. While there are many food items for which you don't need much magnification, such as anything that fills a whole plate, it will become relevant when you want to concentrate on some detail or have a smaller item (such as a cookie or truffle).

Also, since macro lenses are usually in the moderate telephoto range, you will benefit from their narrow angle of view, which helps to keep unrelated objects out of your picture (there always seems to lot of stuff around where food is).

Typically, you won't be using very wide aperture, since you are shooting from a close distance and want to keep depth of field above minimum.

For example, let's take this shot:

It was taken with Sigma 28mm f/1.8 Macro lens. Despite its fancy markings, it's actually not a very macro lens, providing maximum magnification of 1:2.9. I shot at minimum focusing distance, and still wished I could get a little closer. The crop factor of sensor narrowed the angle down to 42mm equivalent, but I still had to aim carefully so that people and chairs on the background would not be distracting.

So, in conclusion - the most important factors are focal length (giving narrow angle of view) and magnification (which is obtained thanks to relatively close minimum focusing distance at that focal length). Sure, you can do food photography with non-macro lenses, but you'll have to work harder to find a suitable angle and composition. In post-processing, you can simulate both of these properties (at cost of resolution) by cropping.