Meanings of rivalrous in English

Poolside this week and the atmosphere is raucous and rivalrous.

Most products are rivalrous (scarce) - zero sum games.

I understand this, as I know what it is like to always come last in a rivalrous family.

Similar thing with Weekend Update, which is in a way a kind of, do you feel rivalrous with... Jon Stewart at all?

There had always been some sort of rivalrous edge to their conversations that he didn't understand, but which seemed to involve Rose.

He can justifiably cite genuine achievements during that time in Uefa's HQ, besides longevity of survival, itself a feat in a highly rivalrous environment.