How can both have the right to intentionally kill each other, when it is practically impossible for them both to do so?
It's not so much that they have a "right" to kill each other. They have a right to survive, they have a right to pleasure, they have a right to food, they have a right to space, they have a right to movement, etc.
Pretty much, in nature...any reason someone would kill another person is just fulfilling a right that someone naturally has.
In the state of nature, humans have the natural right to persue anything they wish on their own. They can say whatever they want, believe whatever they want, do whatever they want, experience whatever htey want, eat whatever they want, etc to such a degree that they can do those things themselves.
They have no NATURAL right to have their rights protected from violation, because that requires something from another person. They have no NATURAL right for their rights to not be infringed upon, as that requires something from another person.
In the state of nature, ones natural rights are protected only to the degree that you can protect them yourselves...and that's it.
It's only through a social contract, and thus agreement amongst multiple poeple, that the artificial concept of ones rights being protected comes into creation.
A right entails absolutely ZERO obligation upon someone else. Indeed, if there is an obligation to another for you to exercise your right then it wouldn't be a right imho, or at least not a "natural right". A natural right is innate within ones self.
That is one of the primary benefits of the social contract; the agreed upon protection of some of your rights through the agreed upon limitation of other of your own rights.
A right to life doesn't mean simply that you have a right to live and no one can take it from you. It means you have a right to strive and take any action you need to in order to remain alive. If that means killing someone else to take their food so you don't starve, that's absolutely fine within the state of nature. It's only through a social contract that your "right to life" must be respected by others within that contract, in exchange for you being required to respect theirs as well.
A right entails an obligation. You have a right to life, so I have an obligation not to kill you. You have a right to property, so I have an obligation not to steal from you. And so forth. If rights do not entail obligations, then they are pointless.
As it was famously said, life within the state of nature is solitary, poor, nasty, brutish, and short. It is a war of all against all.