Keep at it then!
The Copyright for your video should always be at the beginning or end credits of your video:
©year by Your Name (or Your Company Name [or both])
for example:
©2019 by F•X Mahoney | Sight-Creations (my d.b.a.) — it only needs to appear once and it doesn't have to be on the screen long (mine are usually about 1 second). It's just a "tag". It needs to be IN your video.
😎 I don't see the same problem you do. I'm saying: Go for it. Apple's EULAs are almost all the same from Apple Loops, Jam Packs, Motion Templates, everything I've seen (and again — I cannot find anything about the use of emoji on Apple's site anywhere.) As far as I know: Apple doesn't go after its users. Period. As an argument in your defense (for using them in your video): Emoji, on Apple machines, are provided as a Typeface with a specific "character set". Typefaces are not copyright. Anyone can make a Typeface of any "font family" ever made. I used to do this back in the 80's and 90's. As long as the artwork is your own*, the generated typeface is your property. That accounts for typefaces by Adobe, ITC, and many other font foundries copying each other (every foundry has a Garamond, Futura, etc...). The letterforms themselves cannot be copyrighted. If Emoji are provided as a font, then they are letterforms. They are in common use with specific meaning. Even the "pile of poop" (💩). Now if you were to just copy the emoji characters from Apple Color Emojis and build your own font — and sell it as your own — then you'd be in a heap of trouble.
Also, I hardly think Apple would have put this up:
https://support.apple.com/en-us/HT207861
If they didn't want you to use them in your videos.
And you may find some comfort with this article:
http://ideas.dissolve.com/tips/how-to-get-emojis-in-your-projects
there's a section on "Do you need to license emoji."
*By artwork, fonts are created with "vector" shapes. There is an infinite variety of ways in which the outlines of character shapes can be created. It's like fingerprints. As long as you manually create the shapes yourself — even if it's a dead ringer for another person's font, it's your artwork and you have those rights of ownership. But you cannot copyright the actual forms of the letters if you understand the distinction. You cannot copyright the letter 'i' in such and such a font, but you can copyright WHAT you did to create that letter i.