There is no secret ingredient, Yandex just put more effort into supporting languages that are spoken in ex-USSR countries, because that's the most important market for them.
Other translation tools do not consider i. e. Kyrgyzstan an important market therefore do not put much effort into supporting Kyrgyz.
Other translation tools do not consider i. e. Kyrgyzstan an important market therefore do not put much effort into supporting Kyrgyz.