Ok, this is my query:
SELECT video_category, video_url, video_date, video_title, short_description, MAX(video_id) FROM videos GROUP BY video
I would try something like this:
SELECT s.video_id ,s.video_category ,s.video_url ,s.video_date ,s.video_title ,short_description FROM videos s JOIN (SELECT MAX(video_id) AS id FROM videos GROUP BY video_category) max ON s.video_id = max.id
which is quite faster that your own solution