I take the Google quote to be a jab at Russia in terms of homosexuality.
But that does raise the question -- what makes something a right and how do we have them? Here, there are several theories that are distinct.
First, the basic definition of a right is something that I should be permitted to do or something I can obligate others to do for me. In the example, Google is pointing out that according to the Olympic Charter, everyone is to be permitted to engage in sport.
But then why/how do we have these rights?
natural rights - on a natural rights view, the rights are there if we just look at things in the world. You can find this in the writings of Locke and Rousseau and in the US Declaration of independence:
We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.
In a weird way, Kant is also a believer in natural rights, but here the "nature" is that we are rational beings. In each such view, there's a concept of what humans are and how they are to be. The danger of this view is that it depends on contested accounts of human nature and their interpretation to come up with rights.
The competing theory is that rights are granted by society. This is sometimes called legal rights but there are definitely other ways of granting rights that are non-natural. Hegel sets the stage for how this type of theory works. His central example is property rights. Property rights only exist insofar as we make them actual by recognizing that others have a right to property. If we just say they do, but we take it arbitrarily no such right exists. (See my answer here for a discussion of how Hegel's idea of rights works). Simply put, on this type of account, we have a right because society says we do. The incumbent danger is that if society grants rights, it seems equally capable of being a mob that takes them away.
There are also other accounts of human relationship that do not depend on rights. This was the classical account. Thus, we don't see Plato or Aristotle talking about rights even though they have lots of beliefs about how people should treat each other. There has been a decent amount of literature in recent years from the New Confucians (20th/21st Century Confucians) talking about how to organize a society without using rights as the basis or how to get many of the benefits without some of the flaws. One key reason for avoiding rights-talk is that rights impose an obligation and then invoke a legal solution such that I sue you when you violate my rights.