Chromecast with Google TV and newer Google TV-branded sets handle sideloading a little differently from plain Android TV. Here's the version that actually works.
Google TV runs on top of Android, so the same APK works fine — the permission flow is just arranged differently than on a Fire TV or generic Android TV box.
On Fire OS, you flip one global "unknown sources" switch and you're done. Google TV instead grants that permission per app, and it won't even show you the option until an installer app — Downloader, in this case — is already sitting on the device. That's the part that trips people up: they go looking for the toggle before installing Downloader and can't find it.
Search "Downloader" — it shows up under the AFTVnews developer name.
Type it into the address bar and select Go.
The first time, Google TV will interrupt with a permission screen specifically for Downloader. Tap Settings, then enable "Allow from this source."
Downloader resumes and the install prompt appears normally from here on.
Find it under your apps, alongside everything installed through the Play Store.
If the permission screen doesn't appear automatically, go to Settings → Apps → See all apps → Downloader → Install unknown apps, and enable it manually.
Aptoide