They are still the most popular search engine in Russia, they have the best brand, etc. Intangible stuff like that is hard to copy. Running a search engine on the scale of Yandex is very expensive so I don't think that they are going to be replaced by some startup that copies their code and adds a few features. Probably a bunch of bugs will be found but that's not the end of the world. Apparently they handle images pretty well so parts of that may be (illegally) copied in some places.