I think it is, actually. This method of dealing with women who speak up - veiled threats, sniping about "tone," complaints that 'we're not being treated fairly!' - is the actual root sexism. It's not just a PR problem or a problem with complaints. The anger here focused directly and solely on the woman who made the complaint, in an ugly and crass way, and that qualifies as more inherently sexist than anything in the video.
Well... no, because the anger would have to have been because she was a woman rather than just directed at a woman. Being angry at a woman isn't sexist.
I don't see any evidence that the responses were that gender-specific. If I'd made similar complaints they might have also called me out on my tone.
Sexism is not about intentions. Neither is racism, for that matter. It's about the effect our actions have in the world. I can be a non-racist and say racist things; I can even say racist things accidentally or inadvertently. That doesn't make them less racist. Likewise, I can consider myself enlightened, and mean absolutely nothing sexist by it, and still let my girlfriend do all the housework, or say things that I don't realize are hurting women in general.
That can be little scary, I think, because most of us are at least a little worried that we're going to get accused of something terrible and be held up as guilty of sexism or racism. But there's something freeing about letting go of that and accepting that everybody can make mistakes. The fact that you say something sexist doesn't make you a sexist. The point is just to try to stop doing and saying things that harm the status of women as a whole in society.
And in this case, yes, this harms the status of women as a whole in society. I'm pretty sure that Christian Sanz and Rueben Katz are perfectly nice guys who don't catcall women on the street or abuse their wives or girlfriends or whatever. I'm sure, in short, that they're no sexists. But that doesn't change the fact that this event is part of a pattern that is endemic and that makes it very, very hard for women to speak up when a company does something wrong. The pattern is laid out clearly by one of Shanley Kane's tweets: distract people by focusing on "tone" and saying you're not being treated fairly, and then make subtle economic threats.
Regardless of whether or not Christian Sanz or Rueben Katz are themselves sexists - I have a feeling they're not - this pattern is patently sexist. And it needs to stop. It's a pattern that's been repeated over and over again. We can't see this one incident as completely divorced from the millions and millions of other incidents where women have been gaslighted ('calm down already! why are you so upset?') and then threatened with economic hardship.
On the whole, I think the guys involved in the conversation end up looking more stupid and petty, especially given they are cofounders. Now, am I sexist in saying this? Does everything have to viewed from those lenses?
You can try to reason with people or you can just have a bad attitude and smack them and hope the other will bow.