Essentially that’s the try_files pattern.
The php_fastcgi directive should already be doing that for you though. See the expanded form (the rewrite @indexFiles is the “long form” of the try_files directive… which uses the file matcher with the try_files option)
The {query} part is to preserve the request query (the bit after ? in a URL) after the rewrite, because otherwise it would be lost (i.e. copy it from the original URL into the rewritten URL)