1. Most (all?) written languages are linear -- they are processed sequentially by the brain and then deeper meanings are extracted (particularly wrt metaphors and allegory, but also viz. complex sentence structure). Emoji are not unique on this count.
2. Paper and pen (the surfer example) also have technological constraints. It's a "2D" surface, width of line, etc.
3. The input difficulties of emoji today seems temporary. For example, a gesture interface to get you to the correct emoji.
4. What about non-alphabetic written languages?
These seem like obvious first-order responses to the article, so I suspect I'm missing something (besides my first cup of coffee).