If it runs the query through DDG's server side, then Google would just see at as an anonymous query along with a million other anonymous queries coming from DuckDuckGo's servers.
Unfortunately, that's NOT what they do. Instead, they just forward you to the google search result, which is pointless and stupid.
Not so. The point is that you can set DDG to be your default search engine, and put !g anywhere in the search string to search google in case you need it.
Can you elaborate? It just does the same query on Google, how is it preventing leakage of information to Google?