Recording views is very simple, simply add a row to a table that represent the "view" action. This is fast because no locking is required in the database, you're just adding a row onto the end of a heap.
Aggregating that into the total number of views requires something like doing
SELECT COUNT(*) FROM ... which means you have to lock the table while the calculation is progressing. Alternatively,
UPDATE ... SET num_views = num_views + 1 also requires that you lock that particular row every time someone views it.
So from a scalability point of view, it's much more efficient to add a row each time someone views the video and then do the
SELECT COUNT(*) FROM ... every ten minutes or so.
Note I don't actually know the architecture of YouTube, or whether they even use a relational database to store their data, but whatever they do use, the principle is likely the same: inserting data is cheap, aggregating values is (relatively) expensive.