(Disclaimer: Google employee, previously unaware of this program until it showed up on HN, speaking for myself and not the company.)
My guess is that this is trying to advocate for the open web, draw attention to all the ways that the web has changed our lives, and brainstorm new ways for it to continue impacting lives. It feels like the open web is under attack a lot these days, from various angles like walled-garden social networks, proprietary app stores, spammers, etc.
Remember that the vast majority of Google's revenue still comes from AdWords and AdSense. The more people use the open web, the more they search, the more they click on ads, and the bigger Google's revenue. Also, the more data that's available to Google and the better their algorithms can perform, which lets them put out better products.
When people use the open web, Google's stock price rises with no extra effort needed. When people switch to proprietary products, it's an existential threat to Google's business model.
So yes, this is done out of self-interest, but it's a case where a corporation's interests align with consumers. As a user (& a potential startup founder in the future), I very much want to keep the Internet free & open.
I very much understand the motivation behind it, it's just the means that is shockingly tacky and uncharacteristic. A slogan contest for the importance of the open web? Really?