So I think the confusion might come from what "first" and "last" name mean?
In more universal terms, "First" name is the name you are called when your friends or parents want to address you and "last" name is surname or your family name. Middle names is whatever name or names appear between those two names.
So with that in mind, I would believe that you still only write your "first" name in the spot. But as Matt said, a travel agent (or even a call to Royal) would be best to sort that out for you.
Indian and US passport has field “Given Name” on passport and no separate middle name field. My Given names field has middle name but my cruise reservation doesn’t include middle name, will that be fine?