What version of InDesign are you using? Are you making reflowable EPUB or Fixed Layout EPUB?
Usually EPUB videos are viewed inline and not full screen. It may depend on the particular EPUB viewer.
You should prepare your video as an MP4 with H264 encoding.
If you're testing on Adobe Digital Editions, make sure you're using the latest version (4.0.3).
I use Indesign CC
I make a fixed Layout EPUB
my videos are encoded in MP4 with H264
No problems for me creating a video and playing it on iBooks on my iPad. iBooks will display a controller by default. You will have no control over how it displays or works.
I created it in InDesign CC 2014 and used the default settings.
What's the question?
Can we change the controller?
I want to play the video by clicking on it - no controller.
As on Youtube, it is possible to play or stop the video just by clicking on it.
No. EPUB display is controlled by the EPUB viewer. Different viewers display videos in somewhat different ways. Controllers are usually shown, and there is no way to disable them, sorry.
I think...and I'm not sure...if you hack into the markup you can disable the controller by removing or changing controls attribute for the video tag.
Not sure if this helps you, but I created a couple of buttons below a video and set the playback under the option for "video" in the button palette. One controlled play and the other stop. It worked pretty well on Android but there wasn't an option for full screen.