No, you don't need any other DNS servers to use Simple DNS Plus.
The Internet DNS system is basically a BIG tree of DNS servers which are all connected, and at the root of this tree are the "root" DNS servers.
Simple DNS Plus comes pre-configured with a "root file", which is a list of the 13 "root" DNS servers on the internet.
For example to find "www.volvo.se" (the web server for Volvo in Sweden), Simple DNS Plus does the following:
1) Ask one of the 13 root DNS servers for the addresses of "se" DNS servers.
2) Ask one of these "se" DNS servers for the addresses of "volvo.se" DNS servers.
3) Ask one of these "volvo.se" DNS servers for the address of "www.volvo.se"
By iterating through the tree (starting at the root), Simple DNS Plus can find any address in the world based on this "root file".