The cold war was full of hot wars where the US and USSR fought by proxy.
They're both directly involved in this one, there is no proxy.
To the contrary: neither is directly involved. Neither the US nor Russia have troops on the ground in Syria.
They've both been bombing various factions, that's direct involvement. The both also have troops on the ground, the US has them in the north with the Kurds and the Russians had personnel at the very airbase that was bombed.
All we need now is an arch duke in an open top car.
You think Russia wasn't propping up the North Vietnamese during the Vietnam War?