There is some confusion here.
First, maybe you know but the ARC app itself does not support Chromecast built into the ARC app:
You can, however, run ARC on the Android tablet and then use the tablet’s Cast feature to cast the tablet’s audio to the Chromecast receiver. This works.
However, if this is what you do I don’t understand why you “have no idea is this is working via Wi-Fi, or Ethernet.” If using Chromecast, you would have to choose Cast on the tablet and pick the receiver from a list, so I think you would know. If using Ethernet, you would plug an Ethernet cable into the tablet, so I think you would know as well. Plus, Ethernet is not an audio protocol, it is just the basic network layer over which you would use an audio protocol; the same applies to Wi-Fi - i.e., Chromecast would work on top of the network layer.
Maybe you can tell us what exactly you are doing and then we could understand what you are using.
Second, if chromecasting to the Wiim, it does not matter whether the Wiim is Roon Ready or not because you are using Chromecast. Roon Ready means support for Roon’s RAAT protocol, which is used instead of Chromecast but works only with full Roon on the LAN where the Roon Core is, not with ARC remotely.