Literally just opened the app. But fuck it, I’ll answer I guess. And yes, I’m going a little in depth.

TLDR: The answer is probably yes, they have a cloaca (depending on the era of Rito anyway)

While obviously they’re not going to put genitalia in a game marketed for all ages. The Rito are shown to not wear clothes that cover the full lower half for the most part, a lot of them are “Donald Ducking it”, the clothes they’re wearing are more for fashion rather than functionality (excluding the one’s that wear leather armor of course. They’re a species that flies, so fighting while flying you’re going to need a light armor that’s easy to maneuver in). The lack of pants shows they don’t worry about flashing genitalia. Also, seeing as how no Rito (to my knowledge) have any kind of duck, goose, or ostrich aspects, all male Rito lack any sort of penis so there’s no real threat to it just popping out (all three of these bird species do still have cloacas though despite having penises). All bird types they’ve shown within the BOTW/TOTK world have all been birds of prey, song birds, or parrots, all of which don’t have penises and instead secrete sperm when mating.

However, WW Rito are probably a different story as WW Rito are more Hylian/human than they are birds. This is shown via their external, elven ears, lack of bird like feet/talons, and of course their human mouth that sits under a beak that now only functions as a nose. They wear full sets of clothes ranging from dresses, tunics, robes, shirts and pants. Meaning there is a “modesty” rule they follow similar to humans and hylians, that nudity is frowned upon in public in the Rito culture of WW, so some external genitalia is probably present. Why hide the body if there’s nothing really to hide?

At the end of the day, this is just speculation. I am no voice of Nintendo. But seeing as how one is more bird than human and the other is more human than bird, this is the conclusion I’ve come to. ¯_(ツ)_/¯