The word "territory" in Balaji's one sentence doesn't refer to a territory that you have to defend with a military. It might be as small as a single club, or it might be a special economic zone like Prospera in Honduras. The lack of sovereignty of the physical territory is not a problem, as some recognized entities like the Hospitalier order have no sovereign territory at all. For a network state it is the sovereignty of its digital part that matters. And you don't have to aim for diplomatic recognition at all, it's all in Balaji's words "a toolbox".
The network state is not at all what you think it is. It's much closer to your idea of building our own institutions.
The network state feels reminiscent of securing jepgs on the blockchain.
Indeed, and by the way this is the pursuit of some Bitcoiners as well (example: raretoshi.com). And as soon as your institutions will need gated access, there will be NFTs or dont-call-these-NFTs-although-they-are and they probably will come with jpegs attached because everybody already expects it anyway. Also, punk6529's JPG thread is helpful to read regardless of whether you agree with him or not.