They should get a refund because it's just good business.
Sure, it wasn't the theatre's fault that they didn't get to see the movie, but it's not their fault either; delivery isn't scheduled down to the minute unless you're having a planned induction or C-section in hospital, and there's a margin of literally weeks on either side of a woman's estimated due date where she could end up giving birth. Braxton-Hicks contractions (which are basically your uterus lifting weights in preparation for the Real Thing) are hard to tell from actual labour starting, so you can be well on the way to having your baby before you realise that it's actually happening... like my sister, who was in first-stage labour for over 24 hours, got told it wasn't time yet, and ended up giving birth to her second child in the bath when the ambulance didn't get there in time to take her back to hospital once it was obviously time. It's not reasonable to expect a pregnant woman to restrict her activities to stuff that can be broken off in a hurry without financial penalty as her due date approaches. I say this counts as circumstances beyond their control.
If the manager had given them a refund - even the partial refund they were asking for, not a full one - without an argument and waved them out the door while wishing them luck and congratulating them on the imminent arrival, they would have ended up with a good story to tell that showed the theatre in a positive light. They would have gone back, to see different movies if not the one they'd had to leave. Now? That's "the theatre with the jerk manager who kept us talking until [child] was nearly born on their floor". They've still got a good story to tell, but it's not positive; they're more likely to go elsewhere when they want to see another movie, and they might influence their friends and family away from there too.