Yes it has to be a video on iOS device. They rejected the app again saying :
Second time:
"Specifically, it may be appropriate to provide us with a demo video that displays the full functionality of the app while displaying a proper iOS device."
First time:
"We began the review of your app but are not able to continue because we need access to a video that demonstrates your app in use."
It looks like some Apple testers are not provided an iPhone with working data plan. So when an app requires to have an iOS device for field test (e.g. an app used for finding places to eat in 1/4 mile radius, outdoor activity app - running routes, biking trails, etc.), the tester has no way of knowing whether the app works or not, unless he/she sees the video. The other reason may be they just don't have time or don't want to do field test.