On Android TV, the Play Store updates silently through Google Play Services. Check: Settings → Apps → Google Play Services → Manage space → Clear all data (then reboot).
This specific APK was notable for bridging older hardware with then-modern software capabilities: google play store android tv 75 08 apk
: Use a USB drive or a cloud service like Google Drive to move the APK to your TV. On Android TV, the Play Store updates silently