Can running a video over ethernet be split?
Not with those boxes, but the broadcast industry version of video over IP (SMPTE 2022-6 and the 2110 suite) can do this as they are actually IP Multicast based. 

The gotcha is that they typically run uncompressed so you are looking at up to several Gb/s per multicast flow (4k60 you are looking at 12Gb/s), and you really want non blocking switching fabric. 

It does work, but you will hate the price.  

HDCP with consumer gear is also a bit of a pain (There are ways around that however).