What are the key points in arguing for a world religion such as Hinduism?
I would make the argument that part of Hinduism's fundamental appeal is that it does not seek to overtake other religions, but rather complement them. Hinduism is rooted in the idea of Brahman, a universal and "unchanging reality" in the midst of temporal conditions. This Brahman is a transcendent entity that encompasses all that which seems different as part of a universal entity. It is here in which one can see how Hinduism can operate as a world religion, embracing other spiritual narratives in its own.
In his Second Address at the Parliament of Religions in 1893, Swami Vivekananda related a story about a frog in the well. The story deals with a frog in a well, convinced that his well was the biggest in the entire world. One day, a frog who came from the sea came into the well and started talking to the other frog about from where he came:
"Where are you from?"
"I am from the sea."
"The sea! How big is that? Is it as big as my well?" and he took a leap from one side of the well to the other.
"My friend," said the frog of the sea, "how do you compare the sea with your little well?"
Then the frog took another leap and asked, "Is your sea so big?"
"What nonsense you speak, to compare the sea with your well!"
"Well, then," said the frog of the well, "nothing can be bigger than my well. There can be nothing bigger than this. This fellow is a liar, so turn him out."
Swami's point was that this disagreement is the fundamental problem with the world's specific religions. They seek to only talk about "their own well." When one sees how Hinduism's embrace and fundamental notion of Brahman seamlessly integrates all "the other wells" into "the sea." Hinduism views consciousness as "the sea" and seeks to transcend the condition of the "wells" that limit all human sight. Hinduism can be seen as a world religion because it stresses the idea of the sea and not the well. Swami's story would be a reason for why Hinduism can be seen as a world religion.