“Bytes” is not an arbitrary definition in the contest. Any use of an emoji takes 4 bytes. Some of these new combined ones can be 25+ bytes when accounting for zero width joiners, variant selectors, and modifiers. Technically you can pack nearly as much data as you like into a single legal Unicode glyph (think infinite zalgo text) if you just want to have the thought experiment.
Unicode is a nightmare, but I’m glad everyone agrees to share the same nightmare.
Go have a look at https://beta.dwitter.net - many of the examples there use this technique to fit more than 140 bytes into the "dweet" (many are also less than 140 characters, so don't need to use this compression technique). There is a convenient "compressed" switch to "decompress" the code. The rule on dwitter.net is no more than 140 characters (not 140 bytes).
I wonder these days if anyone is using multi-character emoji (don't know what do you call those exactly) to compress more data in 1024 "bytes"?
Since HackerNews does not allow emojis, here is a demo of what I mean:
https://output.jsbin.com/nebemihuhe
[1] https://js1k.com/2013-spring/demo/1426