What is this HDMI gadget name ?

Hello. Is it a wireless hdmi extender, a repeater, a hdmi wireless link, a what ?

A television gets its input from a "TVbox" into its HDMI wired port. What are the red items pair below inserted/added ?

ethernet---------------->TVboxHDMIout--------------->wiredTVhdmi

In other words, a gadget with HDMI input and HDMI output also transmits wirelessly to other room to feed a second TV HDMI jack. Nothing to do with WiFi at all becoming :

ethernet---------------->TVboxHDMIout-------------->wirelessHDMItransmitter----------->wiredTVhdmi input

Plus:

WirelessHDMIreceiver----------------------->anotherTVHDMIinput.

HDMI wireless video transmitter
+
HDMI wireless video receiver

Typically sold as a matched pair. HDMI cannot work with one transmitter and multiple receivers. Cheap sets for 1080p and 30' transmission will cost about $50 and good ones for 4K video and 1000ft transmission will be about $400.