Interesting thread, hadn't noted it before.
Before telegraph and the Transsiberian railway I doubt if Russia could seriously put much weight behind a presence in Siberia or anywhere near at all. But Asia Minor, Black Sea, Caucasus, Afghanistan and perhaps even India might be another matter. Without Peter's urge for becoming western ASAP I could imagine Moscow rulers (with pre Peter look) turning their full attention to the south and southeast.
Against the Ottoman they will have their hands full, especially if not military reorganised along western lines, so this could draw out into a looong conflict. They risk meeting the British sometime too in Afghanistan or India. Chistianity (Ortodox) will probably be advanced more into Central Asia in this ATL, and if the Russian "Crusade" against the S and SE goes on it might even include Constantinople. I could imagine this Russian orientation being coupled closely with a greater focus on the Byzantine heritage claimed by the Zars long before Peter.
In Europe things might develop quite differently. First the southern coast of the Baltic Sea will be dominated by one or more N. European powers. If the PoD is Peter never happening Sweden at first glance appear to be the best bid for a dominant power in the Baltic, but it must not be overlooked, that Sweden in the Great Nordic war already had its hands full and never really had sea supremacy, not in the W. Baltic anyway. Of course having Karl XII at home will be nice, but that is no guarantee - Frederiksten is still there.
By early 18th century Poland had been at least temporarily broken, but relieved of the presense of a westward oriented Russia and perhaps even a Prussia Poland might be seriously back in the fight later. They were underway with interesting development in late 18th century.
Until then Denmark-Norway will still be the main rival over Baltic supremacy, supported by various European allies. I could imagine Denmark-Norway settling in Pommerania and Sweden in Finland, Ingermannland (no St. Petersburg) and Estonia. Poland and/or various German principalities (Brandenburg, Saxony) could be bidders for the area around East Prussia.
The European sea powers will probably (as usual) see to that no power gains control completely over the Baltic entrances, so one power dominating the whole Baltic is unlikely (need an earlier PoD).
Regards
Steffen Redbeard