I wouldn't expect a big improvement in average performance but the long tail of high latency cases should be improved by avoiding head-of-line blocking. Also peer-to-peer should be an improvement over client-server-client in some situations. Not for battle royale though I guess.

Edit: Very cool game! I love instant loading web games and yours seems very polished and fun to play. Has the web version been profitable, or is most of your revenue from the app stores? I wish I better understood the reasons web games (reportedly) struggle to monetize.