There are some alternative ways for AirPlaying to Apple TV. One of them is to directly AirPlay the video. Here's how to do it from the browser:
First, you'll need to open the video on Safari to be able to use this feature. After playing the video, you'll see the AirPlay icon:
You can take the same steps while using Safari on your iPhone or iPad as well.
The other way is to use AirPlay Mirroring on your iPhone or iPad. Here's how:
Activate AirPlay by swiping up on your iPhone or iPad and selecting "AirPlay Mirroring".
It will start to mirror the screen of your device.
But when you launch a video from the browser, as soon as the video starts playing, the Apple TV stops mirroring and starts playing that video.
You can be sure of that when your device's screen looks like this:
You can select subtitles by clicking the speech bubble icon at the lower right.
Have fun! 🌮