Fix player-enter events to use complete info_json() method

Previous to this commit, the player-enter event was hardcoded to send
only ID and name properties, which was enough for an actual new
player. But a player-enter event can also happen when a player
re-joins after being disconnected. In this case, we want the score to
be sent as well.

We can get everything we want by using the player's info_json() method
rather than doing a custom call to JSON.stringify with a hard-coded
list of properties.