net socket request never arrives

In your Espruino code running on the ESP8266, we might try adding:

socket.on('close', function() {
   console.log("Socket closed!");
});

it may be that there is an underlying socket connection error. Although I don't have any experience with it, another possibility would be to enable the ESP8266 specific debugging with:

require("ESP8266").logDebug(true);

and we can see if additional diagnostics are produced.

I'd also look to see if base connectivity between the ESP8266 and 192.168.0.113 have been achieved using:

require("ESP8266").ping(...)