Yes, WiDi is for video, and anyway, who uses WiDi today?
from Wilipedia:
IntelĀ® WiDi and IntelĀ® Pro WiDi Applications, was a Wireless Display (WiDi) technology developed by Intel, it enabled users to stream music, movies, photos, videos and apps wirelessly from a compatible computer to a compatible HDTV or through the use of an adapter with other HDTVs or monitors. Intel WiDi supported HD 1080p video quality, 5.1 surround sound, and low latency for interacting with applications sent to the TV from a PC.
Using the Intel WiDi Widget users were able to perform different functions simultaneously on their PC and TV such as checking email on the PC while streaming a movie to the TV from the same device.[4]
WiDi has been superseded by Miracast,[5] a standard developed by the WiFi Alliance[6]
My bottom of line iPhone allows for setting up the phone as a hotspot, although I have never needed/wanted to do so. You can likely keep your cell plan and just get a phone that can do the job.
If you want to connect Echo, you need home internet, and since the bandwidth requirements of Echo are minimal, you don't need but the most basic plan; around $10 a month I imagine.