But iTunes 10.7, from 2012, was the last release that supported this. After that, they deleted the "anonymous requests" feature. Now you have to be paired to iTunes with your Apple ID, and it's useless and horrible.
Somewhat surprisingly, later versions of the iOS "Remote" app still supported sending anonymous requests to iTunes 10. So that was basically fine. Abandonware means no features have vanished, hooray. I had to figure out how to continue running iTunes 10.7 on MacOS 10.11+, which was difficult but possible.
But I think you know what's coming next: Apple just pushed out an auto-update of Remote 4.3.1 and they removed the anonymous request feature.
How out of character for them.
So if you still have Remote 4.3.0 or earlier, and you want to be able to request videos, don't ever allow that to upgrade. You'll want to be turning off "Settings / iTunes & App Stores / Automatic Downloads / Apps".
If it has already auto-upgraded on you, you might be able to get the old version back. Look in "Music/
If you know where to find a copy of "Remote 4.3.ipa", not 4.3.1, I would like to know. Nope, it has to be your own copy.
The iTunes Motto: "Fewer Features, Every Day".