definitions confusing me quite a bit in this thread..."cardio" is generally applied to steady-state exercise that primarily works aerobic energy systems, mainly running, cycling, etc. done at a pace that is using at least around 50% of aerobic system.
Hard style swings done at lower rep (10 or less) sets, relying on alactic system mainly, are just not going to qualify as this type of steady state exercise. Also, the "swings" are not using the aerobic system primarily, but it's being used in the recovery phase, so the recovery is the aerobic "work." However, it appears that the combination of hardstyle swings are done in appropriate intensity using the alactic system, followed by an appropriate rest period utilizing the aerobic system to refuel and recharge, can benefit and strengthen the aerobic system over time.
So I'd say the issue is whether hard style swings benefit the aerobic system, even if they're not classified as "cardio." From my experience, and many others in this forum based on WTH posts, regimens like S&S and the A+A programs do give a lot of benefit to the aerobic system, like people going out and running 5K's, etc successfully without practicing running or whatever but only doing S&S, or having increased endurance in MA, etc. that they didn't expect just from a GPP.
Now do the benefits of these programs like S&S and A+A for aerobic conditioning directly compare to the benefits of a smart running, etc. program? I doubt if they'd come close. However, they still can and do benefit the aerobic system noticeably, which is pretty damn good for a strength and conditioning program! And, adding some walking, running, or other "cardio" to it is a win/win for that energy system.
Note: GS swings done continuously with a lighter weight and aerobic HR over a longer period of time, like 45 mins, could be called "cardio," but that's not generally what people are discussing here, and the benefits of that to the cardio system would be more like running, cycling, rowing machine, whatever as it would be a steady state exercise at that energy level.