Why Yandex offers on the results page to search in other search engines, and Google is not?

Because in Yandex, and Google on another. Or what answer you hoped to get?

Just Google confident :)

Because Yandex is respectful to the users, I for example always when you do not find the result on the 1st page, click on search in Google. But start to look all the same Yandex.

Well, at least Google foreign search engine and what is it, to offer one of Yahoo and Bing? With which he is still waging war.
In General, their ideology is not minimalistic, not logical and not practical. Use some plugins, e.g.: A&P Search Tools neiron.ru/toolbar/about.html

Yandex has positioned itself as a search engine in Russian-speaking web, and therefore gives a reference to global search engines, which may in part not specific requests to do better.

And I have it, is such a line at the bottom
"in other search engines: Google Bing Yahoo! Rambler Mail.ru Yandex.Directory"

Google wants to take over the search market worldwide. Consequently, other search engines, inappropriate