You can use the kit you bought though the option I linked to makes it simpler. because it has a HDMI loop in out sockets.
You need a HDMI spliitter like this one.
Amazon product ASIN B085HFPWKQ
A short extra HDMI cable.
Yes you are missing something. The original device I posted a link to would have made it a lot simpler because it has a built in HDMI in HDMI loop out sockets.
You need a HDMI Splitter like this one.
Amazon product ASIN B085HFPWKQ
And a short extra HDMI cable. Connect the Humax HDMI out cable to the splitter in. Connect one splitter out to the transmiiter in using the new short cable. Connect the HDMI cable used to the TV remote end to the other splitter out.
Next question do both TV's have the same resolution. say Full-HD 1920 x 1080 then that will be fine. If the remote TV has a lower resolution then the local TV signal will be downgraded. to match the kitchen TV.
Lastly you will need to set the Humax box (You haven't posted the model number) , digital audio out from surround to stereo. If I knew which box I could be more specific..
If it's a second generation Freesat+ PVR . Home - Settings - Picture and sound - Digital Audio out - Change from multi-channel to stereo