Sure, the method you mention (which is indeed the method used here AFAIK), is used to set up many devices indeed. I have also used it in my products. However:
1) this device, when non-configured, sets up a hidden SSID. So depending on the method you use, you might not be able to see it. It is to that SSID the mobile app connects to, to set your AP's SSID/pwd (and more). So far so good. The non standard part comes here:
2) I was referring to the method used once the init has been successfully done at least once, so after the configuration of the SSID by the mobile app. The fact that it wants to reconnect to the exact IP address that the device that did the configuration had at config time, is rather non standard I would say. To be explicit, the IP address shown at startup (once the setup is done), is NOT the Riden's IP address (that will be via DHCP), but the address it wants to connect to, the address of the device that configured it. You can imagine the potential problems with that. Many people report having to redo the setup from time to time, as can be expected.
BTW, My phrasing above was a bit condensed, with a bad choice of the word "setup", where I should have used "method of operations". I understand the confusion. Edited.
If the module is faulty however, it appears (I have not checked, but see the pages in this thread I referred to) the ESP8266 is a regular non-reprogrammed ESP8266 12-F, using the standard firmware many come with. And if your replacement doesn't work, the stock firmware can be found on those pages as well.