I know this one (as most of my feature suggestions) is easier said than done, and I must also clarify that I'm only making it based on a shallow thoretical understanding on the topic and no real practical experience, so take it with a grain of salt.

I think it would be a good idea to add support and use WebWorkers (aka, multi-threading in browsers) to the engine, not only for possible performance increases but also for some advantages it cold provide, like keeping the game running in the background when the user switches tabs. The renderer could of course be paused, but the game could keep on updating it's internal state (useful for multiplayer games, for example) and in case the user is, for example, waiting for a long action to complete, sound could keep on playing even when switched out.