Just purchesed a e201BH - is said prewired for King WiFI -- has an amplified antenna for the TV -- is this antenna also used for the WI FI booster that can be purchased by King
I'm by no means experienced with your new purchase but have a bit of experience with antennas.
WiFi and TV use significantly different frequencies. Different frequencies require different antenna sizes and sometimes designs. The TV and WiFi systems are very most likely completely different systems.
From what I can tell from King's website, their external antenna is pretty normal for a WiFi signal. About 7-1/2". 5" is about right for 2.4Ghz (WiFi) so their antenna probably has a little bit of gain. They say 32X online but I've yet to find the actual spec.
Anyway, I bet it works fine, but it doesn't use the TV antenna for anything.
FWIW, they do offer directional antennas as well. While expensive (to my wallet at least), they should be the bee's knees if you really need to reach out and touch someone.