What is he actually saying?
Is he saying replace SQL with No-SQL technologies?
TL;DR: Yes (sort of)
In a more recent talk than the one you linked to on basically the same topic he says: "The database is a detail. Why do we have databases?".
He claims database came to be to make data access from spinning disks easier, but in the future "[...] there will not be disks" thanks to new technology and what he calls "persistent RAM" and that it will be easier to store data using the structures programmers use, such as hashtables or trees.
He goes on to predict that relational databases on a whole will largely disappear due to their new competition:
So no, for him it's not only about SQL injection, although he opines SQL is inherently flawed in this regard.
Author's note:
#Author's note: TheThe statements in this post are only quotes to understand Robert C. Martin's view on this topic and do not represent the author's opinion. For a more differentiated point of view, see Robert Harvey's answer.