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No. The program parsed the word "Google" from the question, used an algorithm to determine that the word was the subject of a "What is?" question, and then returned you a link to a website or a paragraph that was specifically related to the subject word "Google" in a database. That is not AI or self-awareness. That's simple programming.
The Google Search analogy is understandable, but with the Google Search algorithm it is not a matter of AI, but of very good programming that knows how to correctly parse the English language to determine what is required by the user. True AI would only use this algorithm as part of it's AI algorithm, the part that parses English sentences.
It would only be AI if the server application behind it was learning in real-time; programming itself to change it's algorithm based on previous interactions with the current user. This does not happen when we perform a Google Search, even though to us it seems like it is happening.