Although the three definitions of “insect” that I found on Google say “any of numerous small invertebrate animals,” the word “such as” makes me think they are just examples, and not necessarily a list. So it seems like a worm or insect is not an insect, but I think everyone will do well to read the definition for themselves 🙂
The first definition noted by Google defines insects as any of such creatures. The second defines them as small arthropods belonging to many orders (of various sizes) that have jointed legs and wings usually membranous feelers and include such orders as Diptera, Neuroptera, Coleoptera, Trichoptera among others.