Too many butterflies to say for sure, but some ideas:
1. If Novgorod still exists, they might get a big share of the northern regions. That's still a ”Russian" state, though.
2. A Turkic Muslim power ("Tatar") might take a big chunk of it if it gets its act together. A big problem for them to overcome is that the various Turkic groups had no unity in this period. Perhaps the Tatars of Kazan (who didn't call themselves Tatars before the Russians identified them as such, to my knowledge) might partake in some nation-building to unite the various groups of Tatar-speaking Muslims into a singular identity, even going as far as to spread Islam to the shamanist Turkic-speaking groups of northern Siberia. This requires nationalism to arise.
3. An independent Mongolian state might extend further to the north, encompassing the Buryats and other northern Mongolic peoples.
4. The Chinese would likely get a big chunk of it, as Sakhalin and “outer Manchuria" were indeed nominally claimed by the Chinese in premodern times. They might eventually get all the way north to the Bering Straight. If butterflies don't prevent the rise of a strong Japanese state, which could still happen if the right cards are dealt, these areas might later be contested with alt-Japan just as Sakhalin and the Kuril Islands were in OTL.
5. If, and this is the biggest if, a huge North American power comes into play, they might get involved in the region as well. Of course, butterflies would dictate that getting anything remotely resembling the United States in such a world where Russia doesn't exist would be highly unlikely, but it isn't impossible given the right conditions. Depending on how strong or weak alt-China is, any Chinese infuence in the region might be an overextension of power and the right timing might allow whoever's controlling Alaska to walk in and take charge. This, presumably, would also be an overextension of power for this hypothetical North American power and eventually lead to a multi-ethnic state based on the local indigenous peoples (and descendants of Chinese, Japanese, Korean, Manchu, and Mongolian migrants).