Who says their domination of search engines is dominant? Isn't Bing starting to gain some serious market share?
Google became a verb which demonstrates a solid position. I was interviewing at Yahoo and was given a project problem. The interview said "Feel free to Google stuff to build the project", I joked back "Don't you mean Yahoo it?" He laughed and said "No, you can use Google. We all use Google here, it's fine."
I think they're pretty dominant