As CEO, it's his responsibility to make/approve the decision to do the layoffs, or not. The buck stops with him. That's all that it means. It doesn't mean he's liable for any hardships.
If "responsibility" only constitutes "I pull the trigger, and I don't care what happens as a result", then that is a fairly weak kind of leadership -- ostensibly not very different from a child doing whatever they want in a consequence-free manner.
I want to believe that "responsibility" not only constitutes "I can make things happen", but that "I am willing to Make Things Right if my actions cause things to go sideways".
If I'm wrong, then we live in a world where "taking responsibility" means "using power", and "I take full responsibility" means "yes, I used my power to do that" and that's Not Good Enough to call such people "Leaders".
Layoffs are a fact of life with businesses. It sucks. I'm sure these CEOs do not enjoy doing it, but someone has it in their job description (i.e. the responsibility) to make those kinds of decisions.
You may have it in your job description the responsibility to do performance reviews on your reports. Those reviews can make or break a career. If you do them honestly and with the consideration they deserve, you should not be expected to personally bear the consequences of giving someone a deserved poor review.
It's too bad we don't live in a perfect world where everyone has a job and is never at risk of losing it. But if wishes where horses.....
If that was what responsibility meant, then by definition any CEO is fulfilling their responsibility.
The moral meaning of responsibility here means that the CEO takes responsibility for the lives and livelihoods of those affected -- which does feel a bit hollow when the CEO presumably is not only not affected negatively, but probably will be rewarded for increasing shareholder value.
As CEO, it's his responsibility to make/approve the decision to do the layoffs, or not. The buck stops with him. That's all that it means. It doesn't mean he's liable for any hardships.