This module is controlled by pulling inputs low. So, it does not matter what the ESP8266 voltage is, as long as it can sink about 2 mA (which it can). No level converter necessary.
I tested the relay and it works if I control it with an arduino or even with a direct 5v in its IN1/IN2 inputs.
I don't know what you were doing, but all the reviews in the link say exactly the same: it is switched ON by logic "0" and switched OFF by tri-state. The schematics posted by one of the reviewers confirms this.