This wasn't how the cold war worked.
To put things in perspective, the closest nuclear war occurred wasn't over Berlin, but over Cuba.
In Cuba, they may have been using a third party, but the Super powers were staring each other straight in the face. It was Soviet missiles, put in place by Soviets and Cubans, for the purposes of a direct Soviet interest, aimed right at America, with an assertion of direct Soviet power, with American intervention possibly entailing an assault on the Soviets as they were a direct party in Cuba.
Vietnam is not the same. Yes, Russia is supplying aid, and even has a few advisers there on a very hush hush basis, but it is not a direct party, and as such, its not the same as Cuba here for the Soviets and Chinese. In Cuba, it was a situation of having a rope tied around your leg, tied to an anchor. If the anchor goes overboard, you may well get dragged with it.
In Vietnam, it's a situation of something happening "over there".
If the Soviets tactically nuked South Vietnam, that'd be different, because the Americans are directly involved in Vietnam. If North Vietnam had Soviet troops intervening just like the Americans were in South Vietnam, and the Americans nuked North Vietnam, it'd be different, because the Super powers are both directly involved. An assault in these cases would be a direct assault on the Super powers because of the way they were involved. In actuality in Vietnam, the Soviets and Chinese are supplying, but they don't have boots on the ground, and they aren't making themselves an actively involved combatant or anything of that sort. They're remote.
Again, they'll jump on the chance to condemn America, but I don't think they'll start WW3.