"There's no intentional or manual effort at Google to promote pinterest."
But there is an effort at Pinterest to promote itself via Google. Pinterest pays Google for online ad aservices. Pinterest is a Google customer. The user is not.
The bottom line at Google is not driven by showing users the "best" results for users. The bottom line is driven by customers such as Pinterest who pay Google to assist them with online advertising.
Page and Brin identified this conflict of interest in their 1998 paper introducing Google, which was originally intended to be an academic endeavor, not to become an online ad services company.^1 According to the authors, (a) the interests of users and advertisers are not one in the same, (b) there are inherent effects on search results if the search engine is funded by advertising, and (c) the behind-the-scenes operation ("technical details") of search engines funded by advertising become largely non-transparent to users/competitors (a "black art").
I reckon (c) is why we get questions like this one from the OP.
I have also seen these inexplicable and useless Pinterest links in Google searches.
1. https://research.google/pubs/pub334.pdf
Quotes:
"To make matters worse, some advertisers attempt to gain people's attention by taking measures meant to mislead automated search engines."
"Up until now most search engine development has gone on at companies with little publication of technical details. This causes search engine technology to remain largely a black art and to be advertising oriented (see Appendix A). With Google, we have a strong goal to push more development and understanding into the academic realm."
"Currently, the predominant business model for commercial search engines is advertising. The goals of the advertising business model do not always correspond to providing quality search to users."
"For this type of reason and historical experience with other media [Bagdikian 83], we expect that advertising funded search engines will be inherently biased towards the advertisers and away from the needs of the consumers."
"Furthermore, advertising income often provides an incentive to provide poor quality search results."
"But we believe the issue of advertising causes enough mixed incentives that it is crucial to have a competitive search engine that is transparent and in the academic realm."