Didn't watch, but I can see the point about making cuts quickly. It's brutal, but if it makes economic sense, then the sooner you swing the axe the more losses you can stop.
As for firing individuals, it depends. Sometimes, people can adjust and adapt with appropriate guidance. I'm a fan of diagnosing the problem and making fine adjustments, rather than shooting first and asking questions later. However, if someone is way out of line, you sometimes can't afford to wait and let them do more damage. That's not necessarily inconsistent with the statement you quoted (i.e. maybe Jim only fired people who really needed to go).
Yeah, though Intel is historically a fickle employer. For a long time, they had a policy of "up or out", where people who didn't get promotions got let go. That, or they'd cut 10% of their workforce pretty much annually, with the idea being to cut low-performers and thereby gradually end up with a top-tier workforce.
However, such practices have been shown to have serious downsides. They tend to create a paranoid, CYA (cover-your-ass) culture with poor teamwork, lots risk-averse decision-making, and short-term thinking. Short-termism indeed might have played a role in Intel's fab failures and their seemingly endless litany of security flaws.
I think another downside is that, in order to attract talent to such a company, they probably need to pay more than average.
Sales team will take the brunt for sure. Marketing, less so because you need more aggressive marketing to get people interested to buy. That's assuming these 2 are separate teams. Sometimes marketing also refers to sales.