The Amazon Fire TV (and possibly other devices) connects to the network via a LAN Ethernet cable, instead of WiFi. You are able to see active LAN games listed in the Friends menu, when you try to join a game you will be given an error message stating "You must be connected to WiFi to play with your friends".
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Mega_Spud, yes, that does look like a similar issue, although the error message was different than the one I received. I re-checked the version number, and it is 0.15.10. Changed above. Thanks.
Since the other bug report indicates this issue was fixed, I will double-check that the latest version has been installed on the FireTV later today, and see if the bug still exists, then I will update here.
This is possibly a duplicate of MCPE-12061. Can you confirm which game version you are using, as version 0.15.90.7 which you have selected is the beta version which is only available on Android currently.