The poll is interesting insofar as it generates discussion and analysis, but meaningless as an evaluation of human empathy. This would be true even if done in standard laboratory conditions. Stated preferences, particularly for issues of morality and self-sacrifice, map poorly to revealed preferences. A study evaluated how many people said they would donate blood freely in the UK vs how many actually did, with tragically predictable poor matching (https://onlinelibrary.wiley.com/doi/full/10.1002/hec.4246).
The actually interesting study would be to complete this poll to people who truly believed that the poll was real. How would people respond. How would parents recommend their children to respond? Would the father really tell his daughter to potentially step into the blender when she could have a guaranteed survival ticket?
I would state with 95% probability that if a) if those polled truly believed that the poll were real; b) that there were families involved; and c) that they could not communicate beforehand then nearly all (if not all) respondents would press red. This may even be true if they could communicate beforehand.
There are many plausible scenarios in which playing games with superficially negative outcomes is wise. The businessman who is facing bankruptcy unless he can deliver a million dollars to his creditors is rational to put his half-million on black.