A mix of truths and strawmanning.
It's true that Hinduism didn't exist 3,000 years ago (and I'll accept that one can make the same argument for Buddhism not existing 2,500 years ago).
That said, neither did Judaism. Israelitism was what David (if he existed) followed 3,000 years ago. Call it Yahwism with Ezra 2,400 years ago. Only 1,800 years ago at earliest, and arguably only 1,400 years ago, after the Babylonian Talmud, did Judaism exist.
Most western scholars of Indian belief today likewise don't claim that the "Vedic religion" of 3,000-plus years ago was "Hinduism." Nor do they claim that "Brahmanism" or "Indian epic religion" of the Gita and Mahabharata was "Hinduism."
But, I think many would claim that by the end of the Gupta Empire, or certainly by sometime within the Delhi Sultanate, something existed that could be called "Hinduism." And, you can't blame colonialism and the British Raj.
Ditto, if "Buddhism" didn't exist 500 BCE, we can say something like it did by 500 CE or so, by the time of Bodhidharma.
And, we can't blame "textualism" for all of this, either, or claim that "textualism" was a western-introduced vice. The Hindu epics were written when they were, by natives of the subcontinent, and studied after that. The Tripitaka was put into writing in this same general era. Even if the Vedic materials weren't all written down until yet later that we know, that may be as much due to problems of manuscript preservation rather than date of existence.
Also tosh for the idea that because the typical Buddhist or Hindu follower, or proto- of each, was illiterate and only monks and priests read these writings, that we can't call the people as a whole Buddhist or Hindu. King tries to analogize with medieval Christianity and the bible and mass in Latin only.
Christian scholars acknowledge the variety of believe, including heresies like Catharism and ongoing pagan folk belief yet confidently talk about Christian Europe.
As for the idea that the subcontinent didn't have "religion," tosh. Once one throws out the false Christian etymology of the word (one of the good points of the book), and goes back to the actual Roman understanding, it was religious indeed.