On more than one occasion, the author says, for example, "if I can argue for so and so negative right, I can equally argue for so and so positive right." This is a logical fallacy.
In addition - which is not the author's fault - he is mistaken that the Declaration of Independence was written by Thomas Jefferson. There is strong evidence - that has me convinced - that it was actually Thomas Paine that wrote the Declaration. Further - while it is possible that Paine had been indirectly (through interactions with other people) influenced by Locke - there is no evidence that Paine was influenced directly by Locke - which the author uses to begin his entire argument.
Also, there need not be a God/Creator for natural rights to exist. Paine could have just as easily have written in the Declaration, "Every man is equal before the laws of nature." If two men fall off a cliff, one a king and the other a jester, they both accelerate downward at 9.8 m/s^2. Since no man is superior before the laws of nature, it naturally follows that at a fundamental level any one man is not superior to the next. Of course, circumstances can lead to different levels of intelligence, different weight, different facial hair, etc. However, fundamentally, no one is superior to the next.
Considering the above, no person can have a just claim to another person's life, and by extension, to another person's property. The right to self-defense - a negative right - naturally follows from a right to one's own life. The author of the passage which you linked made a leap whereby he said that an argument for the right to rape - a positive right - could be made by an analogous argument to that made for self-defense. However, that is not the case, positive rights require the violation of another person's negative rights, and therefore, cannot be supported by the same line of reasoning.
Rights are not bestowed by states. To the contrary, states are established because those that institute them wish the state to help secure their rights. Thus, rights precede state creation and exist independently of them.
Here's a short book that you will enjoy that gives a good description of the nature of freedom:
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