Is it human nature to expect a glove to fit every hand that arises? Words and their definitions are problematic, aren't they? Words like transcendent, numinous, sublime, even spiritual. They are pretty much all we got and religion can't claim exclusive rights to them.
Transcendence has several meanings, only one of them religious. Numinous can mean awe-inspiring. Kant has a concept of the Sublime. Christopher Hitchens uses these words to make the point that you need to go beyond religion in order to fully appreciate reality, not just to understand it rationally but also to enjoy it, to be dazzled by its beauty and order, to exalt in its wonder.
When Hitchens talks about "the transcendent and numinous," he's not referring to anything supernatural. He's also not advocating any type of worship or debasement. He's referring to an appreciation for the amazing insights and workings of the natural order as well as an appreciation for the greater aspects of the human experience.
He's trying to make the case that religion doesn't own these words or concepts. He's also attempting to address the claim that science reduces everything to chemical impulses and nihilism. His position is that atheists are capable of having the exact same types of experiences as believers, and none of them require beleef in anything supernatural or anything unsupported by the evidence. He's saying that atheists are just as capable of feeling self-transcending love or connection to something greater than oneself or true awe. One doesn't need superstition to take part in any of these amazing human experiences.
If you reject the notion that there exists a supernatural dimension, then all religious and spiritual experiences can be understood as purely, physical phenomena. Therefore, when someone experiences a moment of self-transcending love that feels all-encompassing or when someone goes into a desert and fasts for 40 days and 40 nights or when someone takes a pilgrimage to feel a connection to the divine or when someone learns about the natural order and feels an incredible connection to the universe or when someone experiences a piece of art that moves them deeply and inexplicably to feel as if they're part of something larger than themselves, all of these things can be understood as meaningful subjective experiences in a physical, natural universe with no supernatural or spiritual dimensions.
It's difficult to illustrate how meaningful and impactful these experiences are without using language that is typically reserved for usage in explaining religious experiences. After all, people like Einstein and Spinoza weren't necessarily religious, but they definitely had beliefs that could be called spiritual. Not spiritual in the sense that it spoke of a spiritual dimension, but spiritual as in an incredible admiration for the workings of the natural order, the range of human experience, and the mysteries of the universe.
One can reject the supernatural and absolutely still have a transcendent experience.
Here are the Four Horseman talking about the transcendent and numinous. https://youtu.be/9DKhc1pcDFM?si=n2dsCndVCJviEYEn
And here's Sam Harris on his use of the word spiritual.
https://youtu.be/zLKNvBdUtZY?si=utS8kRZtcr7AX8Ka