@Jayace
Hi,
I just tested this with my Chromecast "3rd generation" (running the most current firmware version) and another router model of another brand and I can tell you that this issue is not specific to your TL-WR902.
If the Chromecast is being powered up and run without Internet connection, then it is basically unusable.
Apparently Google doesn't want us to use their Chromecast devices without them knowing. 
However, what I also noticed is that if my Chromecast did have an Internet connection when it was booting up, but I cut the Internet connection to my Wi-Fi router afterwards, then I still remained to be able to connect to the Chromecast and cast to it from my Android phone and my Windows PC (both also cut from the Internet).
I must note that I haven't tested this for a prolonged time and I don't own any iOS devices to test this with.
But perhaps this is still something you could try out when you get a chance and also have the required equipment, even though your Chromecast hardware is different than mine. Power the Chromecast dongle up while it does have an Internet connection and then keep it under power via its USB cable continuously.