It seems like even Microsoft is prioritizing the more successful mobile platforms over its own Windows Phone OS with this one, although that isn't Microsoft's excuse. According to a spokesperson for Microsoft, the reason why there is no Windows Phone app is because "Remote desktop on phones is a relatively rare usage scenario." This (partially) explains why there is a Windows RT app, but no Windows Phone app. However, this is a good time to reiterate that the app released on Thursday does work on iPhones and Android smartphones.
Microsoft confirmed that there is a Remote Desktop app in the works for Windows Phone, but could not speak to a timetable for that app's release. If you're a Windows Phone user, there is an official option on the way, but you can always use an alternative that's already in the Windows Phone Store.
source: The Next Web