The economic definition could use an update, or at least some asterixis. Lin Ostrom's work is worth looking up, if the topic interests you.
Both rivalrousness and excludability can get gray, changing as technology or legality changes. As intangible goods become a bigger part of the economy, this matters more.
Take HN. Is it rivalrous? If I comment on HN, does this diminish others' ability to comment on HN? There isn't a totally black and white answer to this. Usually, no. Other people commenting is actually required for a forum to have value. OTOH, the premise of brigading (was once a reddit thing) is that a bunch of people flooding into a forum can diminish people's enjoyment of it. I suppose you could call that vandalism, but there are plenty of cases featuring various shades of grey. If your mom joins instagram, maybe you can no longer enjoy commenting on salacious pics.
Ostrom advocated for degrees of, rather than binary definitions.
Excludability... Also debatable and shifting. Digital music wasn't excludable for a while, then it was. Anonymous social networks (like HN) are less excludable than real name networks (like FB), but it's mostly a technology problem. It's also a legal question. The idea of making FB and such "common carriers" was floated around, which would make is legally nonexcludable.
Patents are the opposite. The exist to make nonrivalrous, non excludable goods excludable. So does DRM, copyrights. A GPL license turns an excludable good into a nonexcludable, arguably public good.
IMO, a better starting point is scarcity vs abundance.
Anyway, considering the importance of public science, software like linux & the www... I think it's worth thinking about how important the commons/public domain/classification of your choice is.