Note that the JdbcTemplate is not exactly a Strategy, either. In the Strategy pattern the Strategy is an instance variable. I wonder if it's useful to give names to each and every variant of a pattern - and it seems that library creators don't care too much.
I guess the creators of Spring though of the idea behind the template more than about the technical details. The very name of the template method pattern means that its core idea that we have a fixed sequence of actions which is already coded, and a variant part which we want to create and design later.
The use of inheritance is probably somehow a technical detail. The original version (designed for C++, which did not distinguish interfaces from abstract classes), uses inheritance. The JdbcTemplate passes an interface instead. In a way, what is the important and relevant part :