Can someone explain how blocking off access to a beach works here? Is it because the access paths are privately owned?
Lawyers will huddle, and I'm guessing in the end that people will again have access to public property.
(When bullshit arguments are used, use them against an adversary and raise the stakes.)
It was the treaty that gave California to the US, so not really.
Yep (well, maybe, I don't really know. But for the sake of argument: Yep). But dick moves are the type of thing that cause bounds of rights to be changed.
We're not lawyers here (or are, and are already aware that we're not before a court). In a conversation of what actions are tolerable to a society, laws can be changed. Without going on pedantic tangents about this or that, I just want to point out that: in general appealing to the law without making a case for the law looks like circular reasoning because changing the law (or using other, existing, laws to alleviate problems caused by the first one) is within scope of the conversation. That's probably why your post is currently gray.
If your property blocks access to another's property, you have to give up a slice of your land to provide access for the other property's owner. You can't simply buy up all the land around a property and then close off access. This is called an easement.
In this case the other property is the beach, which is owned by the government, no different than any other property. Khosla has no right to deny access to this property just because his home abuts it. The only issue here is an obscure treaty, apparently, but that will sort itself out.