If you want to get the total count for each user, then you will use:
select user_id, count(distinct video_id)
from data
group by user_id;
Then if you want to get the total video_ids then you will wrap this inside of a subquery:
select sum(cnt) TotalVideos
from
(
select user_id, count(distinct video_id) cnt
from data
group by user_id
) d
See SQL Fiddle with Demo of both.
The first query will give you the result of 2 for each user_id and then to get the total of all distinct video_ids you sum the count.