I'm mystified by some of these arguments.
Once conception has occurred, the embryo/fetus will be expelled from the mother's body at some stage. This will either be on time at 40ish weeks or before that. And this will either be when nature takes its course or when humans intervene. And it will either be via the vagina or by CS. If human intervention is required, the woman will usually be given oral meds to bring about abortion if very early in pregnancy. If it's later on, can't recall the gestation right now, she'd be given vaginal pessaries to effect changes to the cervix to enable it to efface and dilate, bringing on contractions to expel the foetus. This process will be pretty much the same as having labour induced and I'm sure many of you know it well. So she will go through labour and, depending on the gestation etc, the baby may be born showing signs of life or not. In England at least the policy, to the best of my knowledge, is still that if signs of life are shown in a 24 wk+ foetus, there will be suitable resuscitation attempts (strange as that may seem for an abortion). Some units with swankier equipment will do that at 22 weeks or so. If no signs of life (meaning respiratory effort really) then that's it. It's quite amenable to a flow chart.
I can't understand your comment MyDcAreMarvel that a C section is safer for the mother than a late abortion and the Bill was abhorrent. Why, if labour has started as the man in the clip said, would any medical professional do anything other than behave as if it's a normal labour? From a physiological point of view, I mean, not an emotional one. Monitoring, giving augmentation drugs if needed, off to theatre if needed.I don't know the stats now but CS was always statistically more dangerous to mother and baby.
And it is legal in England & Wales certainly, not sure about Scotland, to abort at any time up to term if Drs deem it advisable, plus maternal consent unless she's been sectioned under the Mental Health Act, in which case the courts will be involved. When I was a midwife my hospital did therapeutic abortions, which basically means something physically wrong with the foetus, sometimes the mother. If the 20 week scan shows a condition incompatible with life, after lots of discussion etc, an abortion would be offered and it would go down the 'vaginal pessary then vaginal delivery' route. Why is a CS better than that?
And sometimes conditions develop in labour which are potentially fatal for the mother - like chorioamnionitis when the amniotic fluid becomes infected. Of course rigorous antibiotic treatment is given but doesn't always work. The only solution will be to get the baby, which probably isn't going to survive this anyway, out asap to save the mother. There was a case a few years back in the Rep of Ireland about a woman who died because the hospital were trying to follow the law and give equal weight to mother and baby: impossible in those circumstances.
And also bear in mind the You Tube clip is the US: they do things differently over there.