More like rooting for the Kurds. But you get style points for waving the Putin pom-poms.
The Kurds have ceded control of Kirkuk and the surrounding area back to the Iraqi government and aren't in conflict with the Shia militias protecting the oil fields.
So it's more like rooting against the Kurds to have ISIS reinsert itself into the region. Its also against American interests to destabilize the Kirkuk area, which is where the Peshmurga live and is still part of Iraq.