Putin wants to preserve Syria – this is not about Russia-US relations
Putin sees the potential threat to Russia from Isis as bigger and more urgent, because of the number of Russians (many of them Chechens) thought to be fighting with Isis and the threat of jihadism in and around Chechnya. Russia’s desire to combat Isis need not be seen as a pretext for protecting Assad; the converse may rather be true. In Russia’s view, as Putin set out at the UN, the Assad government is all that stands in the way of complete victory for Isis and the de facto disappearance of the Syrian state.
For Putin, the priority is the preservation of the Syrian state. He looks at Afghanistan, Iraq and Libya, and sees western interventions that have resulted in anarchy. He foresees the same for Syria if the west sees toppling Assad, rather than combating Isis, as the priority.