No, the Video app isn't necessary to upload videos to the post, it has own video processing. But you should have the working Cron Jobs. It can be checked via Studio->Dashboard->Server audit, the line there like "Last cron jobs execution" should have the value not so far form now.
Thank you very much, there was no cron job execution due to a mistake in my cron job script. For some reason the path to php was wrong, most probably my mistake since I have installed UNA on my test environment ... It works fine now and thank you again.