Walmart is a store, and sells things. Best Buy is also a store, and sells many of the same things Walmart sells. They are competitors in the market for selling electronics. Competition between them is good, and so they aren't required to advertise each others' stores.
Google is a search engine. Bing and Yahoo Search are also search engines. They crawl and search the same websites. Competition between them is good, and so they aren't required to advertise each other's search engines.
Google Mail is not a search engine. Google News is not a search engine. YouTube is not a search engine. Google Play is not a search engine. These are all different products from Google Search. Thus, Google giving preferential treatment to these products in its market-dominant search engine would be a textbook example of an antitrust violation: using a dominant market position in one market to interfere in the another market. (It depends on the jurisdiction's specific antitrust laws, but it may not matter where the competitors' products show up in the search results if Google is giving preferential treatment to its own competing products in searches for those products or the search terms that would list those products.)