The game is wonderful and I'm so glad it doesn't have chat! My 9yo niece and I played it through side by side and if it had chat or consistent remote player presence that wouldn't have been appropriate.
Absolutely - I love those. I wonder if there are any other simple web games like this that run on mobile with more nuanced interplayer comms as you suggest.
Hearthstone (while not web-based) is a deck building game that you play against others and you can only communicate with a small set of inoffensive phrases that cover broad sentiments. Makes multiplayer endurable, and you can turn them off if you like.