'It seems more likely to me that Putin is pushing it as much as he can to assert Russia's political and military, and economic, dominance, again. '
That is what the corporate media says, but Russia is weak compared to America. America spends ten times more on its military than Russia, America has bases all over the world, Russia has a base in Syria. America is the richest, strongest country in the world despite being the most endebted. No one can challenge America.
Russia and China and Germany etc want to do business, create trade and growth and so does Donald Trump. But some elites stand to lose power as China rises and they want to maintain power.
'I think it's more likely that he wants to mess up relationships with the West and keep the West (including Turkey) out of Syria.'
Yes, Russia and Iran have drawn a red line in Syria. They let Libya go, they let Iraq go, but they won't let Syria go becaue they know that they will be next.