Does iPhone/iPad Safari require 'Accept-Ranges' header for video?
Solution 1:
I found some Apple documentation that says that it does in fact need that for video.
HTTP servers hosting media files for iOS must support byte-range requests, which iOS uses to perform random access in media playback. (Byte-range support is also known as content-range or partial-range support.) Most, but not all, HTTP 1.1 servers already support byte-range requests.
If you are not sure whether your media server supports byte-range requests, you can open the Terminal application in OS X and use the curl command-line tool to download a short segment from a file on the server:
curl --range 0-99 http://example.com/test.mov -o /dev/null
If the tool reports that it downloaded 100 bytes, the media server correctly handled the byte-range request. If it downloads the entire file, you may need to update the media server.
Source: Apple Documentation
Solution 2:
The answer above is helpful, but does not actually answer the question that was asked.
According to the HTTP RFC, the Accept-Ranges header is optional even when byte-range requests are supported.
However, the documented curl check implies that the answer is no: iOS does not require the Accept-Ranges header for video, but does require byte-range support with partial content (206) responses.
Disclaimer: I haven't checked it on an actual device.