How is (을)게요 being used here?
So I was watching an interview and the man doing the interview was asking a korean woman about Korean and how hard the language is. He then said to her “한국어를 배우고 있는 사람들에게 응원의 말 부탁드릴게요.” Which translated to “Any words of encouragement to people who are learning Korean?”

I thought that -(을)게요 is only used when your tell someone that you will do something. However, here, he is asking her to do something for him and for the people watching the video. Therefore, why would (을)게요 be used here if he’s asking her to do something?

Question

How is (을)게요 being used here?
So I was watching an interview and the man doing the interview was asking a korean woman about Korean and how hard the language is. He then said to her “한국어를 배우고 있는 사람들에게 응원의 말 부탁드릴게요.” Which translated to “Any words of encouragement to people who are learning Korean?”

I thought that -(을)게요 is only used when your tell someone that you will do something. However, here, he is asking her to do something for him and for the people watching the video. Therefore, why would (을)게요 be used here if he’s asking her to do something?

Answer

부탁드리다 is an honorific form of 부탁하다 which means 'to ask a favor of something '.

부탁드릴게요 means I will ask you a favor of something. 
It includes the meaning of "I will ask you a favor of something if you don't mind."

Answer

Your understanding is correct but here he is telling her that he will ask a favor of her (will do something).