[MD Longhorn]

You've defined the crux of the argument...

"The runner fails to touch the intervening base or bases ". Intervening means BETWEEN. This rule is meant to allow the defense to appeal an out for a runner MISSING a base. The situation described is NOT missing a base. It is abandoning a base. We don't accurately have abandonment often --- but this is EXACTLY what that rule is written for.

If you think there's no difference, consider the same situation but without it being an end-of-game situation.

No outs. Bases loaded. Batter walks and advances. R1 scores. R2 runs off the field to the dugout. Do you stand around waiting for an appeal, or do you call this runner out? You call her out. If this was a missed base, or there was not a difference between abandoning a base and missing one, then you would have to wait for an appeal. But you don't. She's out right now, without appeal. She abandoned 3rd base.

Similarly, in the OP - the runner from 1st or 2nd, technically (although we often don't bother because it's irrelevant) these runners are out as soon as they leave the field. Appealing for missing a base is irrelevant - they are already out --- and their out was NOT the result of a missed base appeal, which is the rule you're using to say the run should be nullified. No such run nullification clause exists with the abandonment rule.