Does Google accept itself as Search Engine ?

After learning about Google easter eggs, I thought there would be many competitions to Google, and how it tries to maintain its market share. Unfortunately there is a big competition between Google and Bing, as soon as Bing was launched, it occupied 5% of search engine market share, slowly it occupied 30% of market share. This is amazing, but Google somehow got serious on this and was suspicious on Bing copying Google.

Now funniest part of the story is, Does Google consider itself as search engine, today I tried few search in Google and was surprised to see the search results.

Go to Google.com and search for "search", My thought was, since Google is the top search engine, it will come in the search result as top one, but rather I got this strange result. Interesting part is, few months back, Google accused Bing of copying their search results and proved it also, but the top search result for the word search is Bing, then Yahoo, then Dogpile etc etc, I found Google search somewhere to the end of the page. Ok, assuming search is something very common, I tried the next keyword "search engine" and it came to me as a surprise again, Google search never returned back on first page. Does anyone know of this strange behavior? Any reason why this would happen in Google?