I think your example is actually correct. Eating CAN be a noun, but in your example it is a present participle, a type of verb. It would be a noun if eating was the subject, ie: "eating is fun," where it would be a gerund. https://teacherblog.ef.com/grammar-recap-intro-to-gerunds-and-infinitives/
Sigh I think you're right. It's the progressive form of the verb.
That's been throwing me off all day. Thanks for confirming. Grammar is confusing.
