Donald Trump manages to be more sensible on Syria than Hilary

[GUBU]

What aim are they pursuing, that we desire?

Preserving their basing agreements by propping up a client state would be my guess. But in so doing, they're killing a lot of extremists, and yes, non-combatants. We desire the former (that's where our interests overlap, imo), and wish to avoid doing the latter ourselves.

This delivers both our desiderata.

They're not killing extremists, for the simple reason they're not attacking ISIS. Currently it's not in Assad's interest to go after ISIS because the he needs to control are held by the remnants of the original pro democracy movement.