Thank you for looking it up. I should have said that I had double-checked myself so rather than asking a question, I was trying to point out that Reverso generally tags prepositions, conjunctions and possibly other parts of speech as adverbs.
Do you think the two dictionaries that said it was a verb might have given you results for the verb "to include" and its present participle, maybe?
I guess it's not always easy to classify a word, particularly in English, where you can use just about anything adverbially ;)
There's an idea for a new silly wordplay post.