Hi Marko,
You can head to EasyBlog Settings>Media>General>Storage Paths to see where the paths are for storing media files.
Depending on how and where you want to upload, you can choose between Article Images, User media, Shared media to upload videos.
Keep in mind that if you do not want the video to appear to other users on the Media Manager in the composer, then you have put your videos on your user id folder in User Media. That way only the user id containing this video will be able to see this video in the Media Manager.
Hope this helps.