The specific instance in Qatar's case is in providing AC to a stadium, apparently covered, if not entirely contained, and taking advantage of temperature-induced differential density to apply cooling only to where people actually are, rather than the entire enclosed space.

Which might actually be more efficient than equivalent practices of conditioning all interior stadium air in the US.

A difference between outdoor radiant heating (which I also find immensely wasteful) and outdoor AC is that radiant heat, erm, radiates, so you're only providing a sufficiently warm blackbody, and not attempting to change the temperature of an entire space. Surface temperatures (including skin) are increased by radiant heat, but air temps are not: a campfire will warm your hands and face, but not all the surroundings. Since cold isn't similarly radiant, there's no equivalent mechanism.

What this translates to in terms of Joules or kWh per meter-degree of thermal variance for heating vs. cooling, I'm not sure.

When heating you usually turn some energy into heat. When air conditioning you use energy to move heat out of the conditioned space, emitting waste heat somewhere else. If you’re doing it outdoors, it seems like the waste heat is going to make the local environment even hotter, and in the worse case would cause some kind of air conditioning arms race. Outdoor heating doesn’t have this problem.

Given what I’ve read elsewhere about the lives of migrant workers in Qatar, I can imagine a dystopian scenario where stadium visitors enjoy a cool breeze while workers beneath are being blasted with heat. Hopefully they have engineered a safe way of dissipating that heat energy.

Thermodynamically if we take the headline at face value this is absolutely worse in principle, since abstractly the "outdoors" is simultaneously being warmed by waste heat from A/C. If this were the case it is fighting itself and certainly doomed to lose. But reading the article reveals that there is some (sufficient?) separation between the "outdoors" and outdoors in the literal sense.

Exactly. This coupled with the fact that they are trying to use the ducts to only cool the places people are and not anything else doesn't seem like such a bad idea.