Nothing is "required" for Vudu. However Adobe has a minimum requirement now for Adobe Air apps, which didn't exist when the Premiere was created, and the CPU in the Premiere does not meet those minimum requirements. Apps will still run, that's why we have Netflix, Hulu, etc... but they run very slowly and some developers may not want to release their apps on a platform that they believe hinders the user experience.
The Mini however contains a newer CPU that exceeds the minimum requirements and it runs the existing apps much, much, better then the Premiere. If the next gen TiVo contains a similar or better chip, which it should, then more developers may be willing to release their apps for the platform.
Adobe Air is the same platform used for apps on Samsung smart TVs, so most services already have an app that will technically run on the TiVo hardware. So it's either the speed issue or some sort of business issue holding them back. Once the new hardware is released we'll see which it is because speed will no longer be an issue.
Developer for VideoReDo