Interestingly, you do see it on the first page in Bing and DuckDuckGo.

And while I did initially think that might be deliberate (because hey, why bother showing a link to your search engine on the first page of results in your search engine?), Bing and DuckDuckGo are listed when you search 'search engine' in those search engines.

Makes me wonder why Google doesn't list themself here.