I assume that all your posts are come from single.php. WordPress provides has_category() function to check if post has specific category.
So your code on single.php will need to be like something in given below
if( !has_category('video') ){
the_post_thumbnail();
}
where it checks if post has ‘video’ category. And if it is false then the feature image will be displayed. otherwise, it can’t. Hope it will be help you.