

If it’s something like chromecast it’s not sending your screen locally to the device, it’s sending the source URL of the video itself, so VPN wouldn’t make a difference unless it was at the network layer the TV was using. That being said, did you try playing the same videos on your phone or computer without vpn? On cell? On their WiFi? If it doesn’t work at all on any it’s likely geo blocked as another commenter said. If it works on cell but not WiFi it’s likely their network is blocking them

Yeah generally I like to carry an hdmi cable and plug into my phone/laptop when I’m staying at a hotel. The tv doesn’t always have hdmi, or hdmi I can use, but it’s more secure. What you could do is use a service to download the video onto your phone directly with the vpn and then cast that from there, the tv just gets your local ip path, nothing to block, if you’re going that route obfuscate the video name so it’s like video_1.mp4 instead of the YouTube title