There are two separate issues in play. Let's make sure to address them both.

How is calling her sweetie or babe "treating her as an equal"?

Without context, this could be taken the same way as a male subordinate referring to a male superior as man, guy, dude, bro, or similar. It does not convey the respect someone might feel they should be given for their position, but it is also not disrespectful at the same time. It would be properly described as overly familiar. If a boss feels they should be separated by rank, status, position, or similar above their employees (a.k.a. given respect), being overly familiar on a personal level will not be taken well.

The other issue is one of earning respect.

How much respect did she earn from workers by firing almost 10,000 to cut costs? How about when they don't even give numbers? or how about when someone is fired for taking FMLA time?

The article talks a lot about what she did for the stock price, earnings, and how much money she made the shareholders. At the same time, it doesn't talk about her pushing for a living wage, equal pay for female workers, pushing more female executives into management as a priority for her in the business, offering paid paternity leave for all workers, or really anything like that.

Still, even her salary has paled in comparison to several other top-paying male CEOs across industries [...]

No, it talks about how poorly she was paid compared to men who also make tens of millions.

tl;dr She hasn't done anything to earn respect. Respect never given, only earned.