To control current Fire TV devices with Amazon Voice Assistant, you must use the associated voice remote control or a separate echo speaker. You also do not seem to need the dice-like device, and since it has a built-in speaker, you would even hear Alexa's answers, even if the TV is not turned on. The unit will also be able to handle 4K HDR video.
Of course we can not say with 100% certainty if it really is the "Fire TV Cube". As noted by AFTVNews it is also unclear whether "Fire TV Cube" is an official name or something that Amazon has chosen for the moment as the fans call the device in the leaked image. Your best bet is to sign up to get more information and hope that the ecommerce giant will send out one with all the juicy details in the near future.
Update: A reader sent us scans of the manual that came with his Amazon Ethernet adapter, and one of the pages showed an illustration of the Fire TV cube. The rear panel connectors are labeled as "Infrared", "HDMI" and "Power", while the Micro USB connector is labeled as "Network". This probably means that the device can not be powered by the TV it must plug into a power outlet. Between the registration portal and this page in the manual, we see the Fire TV Cube very, very soon. [Thanks, P.L.!]