IOS – Attempting to play video on iOS 7 shows play button with line through

I'm not sure what video you're referring to, as there is no video in your link. But I assume there was a video there when you posted that didn't work.

iOS does only support video-streams in AVC h264, MPEG-4 and Motion JPEG, and only M4V, MP4 and MOV as containers/file extensions. Other apps are allowed to include their own codecs and can therefore play other formats, but most don't. Mobile Safari does only utilize the native codecs and will only play those formats, and HLS-streams.

There is no official way to get Mobile Safari to play other types of videos, and most likely does Chrome as well. If you can get the direct link to the video you could try use VLC or CineX.

Yes it is possible. I am doing it as I write this answer. There shouldn't be an T&C issue as I know it, just check whether your WiFi is properly connected and has enough bandwidth to stream video. Also you can cross check this by streaming something else through one other application.