My Mac: And I find some emoji doesn't display well on my Mac. Check out that Link:
Emoji are a true type font in...
/Volumes/Macintosh HD/System/Library/Fonts/Apple Color Emoji.ttc
Sierra comes with version 12.0d19e1, which doesn't include the newest emoji (the ones that are displayed as square in your screenshot), unlike High Sierra, which shows the font as version 13.2d1e1 and can display those newer emoji.
You can use "Font Book.app" in the /Applications folder to preview the font.