Nobody owns an idea. The only way to own an idea is maintain exclusive access to it (to keep it a secret).
Nostr allows users to own their online identity by maintaining exclusive access to their private key (nsec).
The content created can be copied, but nobody can take away your secret & post as you. Nostr enables users to own their online identity but not their content. Their content sits on relays & web servers & is easily copied.
I believe Jake is suggesting that there's a form of social capital created which resides with the identity. This social capital is built from content & interactions online. I'm not entirely sure that you could call it property though. I can't sell my identity since I can't transfer it (yet). I can share my identity secret with someone else but they can't be sure I won't sell the secret to someone else.
It's definitely interesting to think about.