Can't connect to Arduino Uno + Wifi webpage
I've never seen this sort of board before.  Normally Arduinos communicate with ESP8266's using a serial connection and the AT command set.  I think that is what this board is doing, because it says you will need new firmware if you want to program the ESP.  So you need to find the AT command that gets the IP address.
(Sorry I don't know the command, never used the AT commands, never likely to)