The university in question wasn’t even a university at the time of its inception! The Kazakh National Medical University was established as a medical institute/faculty in the year 1930 and did not even have its first graduates till the year 1936.
One can say that it was a government university since its establishment as the institution came into existence through the RSFSR SP Council’s decision. However, one can truly (or rather officially) consider this to be a government university since the year 2001, which is the year when it was awarded the status of a “National” university.
Most medical universities in Kazakhstan are funded by the government or established, which is why they’re technically public institutions. As the Kazakh National Medical University also comes under one of these categories, it won’t be wrong to say that it too is a public university; thus, a government university in simple words.