Yes, this represents a security threat because everyone who competes will do anything in their power to get the money and get to the moon. When that much money is at stake, cyber warfare tends to be present. Any new research that is found must be secured tightly so no one can hack it.
I'm pretty sure doing all that would cost more than the prize money offered. This is like a modern day "Space Race". Can't they offer an incentive like this to the first group that cures cancer? How big does the robot have to be? If it was the size of a cell phone, would I still win?
The Google award offered to teams who can successfully land a robot on the moon does not represent a security threat to the United States. International space exploration has always existed with other countries. The countries of Brazil, Chile, India, and Hungary are not hostile threats to the United States in space missions or on Earth.
Humans have always had the need to go out and discover. This was true for Columbus, Magellan and the rest. When the national space program stopped, private companies decided to pick up the slack and offer incentives for space development. This is a brilliant way to keep science moving forward.