Is the injection in a NoSQL database architecture also called SQL injection?

Those are called NoSQL Injections instead of SQL injections.

You can find more information about NoSQL injections, in the OWASP Testing Guide.


Is the injection in a NoSQL database architecture also called SQL injection...

No, it is not called "SQL injection" but this is called a "NoSQL injection", you can read more about in an article titled "Testing for NoSQL injection", written by OWASP.

... and is it still part of the OWASP 2013 Top 10, category A1 Injection?

Yes, this is a type of injection and that's why it is also categorized in OWASP category A1.