I wasn't so much asking about relational databases vs key/value stores, but rather why should I implement things like advanced sorting, mathematical formulas, etc in SQL rather than in the application code that fetches data from SQL?
It's simply more efficient? If I have a table with millions of rows, I'm not going to bring down the entire data set on every request just to sort by latest and grab the 10 most recently updated rows that haven't been soft deleted (WHERE active=1 ORDER BY updated_at DESC LIMIT 10).
Also, his examples are like the tip of the iceberg. There are all kinds of things like windowing functions and common table expressions that have so much power to get exactly as much data as you need right at the RDBMS without having to carry that baggage anywhere else.
Anything that deals with the formatting/display of the columns in the result set rows can be done in SQL, but doesn't have to be done in SQL. It's really a matter of convenience to do it in SQL, especially when dealing with multiple front-end languages, because it means that the formatting is done in one place.