What is "modernity" ? There's definitely something to the author's conception of modernity, but the story told in the quotes is only the half of it, as I understand it. Progress for the sake of heightened mastery over the world is definitely one of the hallmarks of modernity, but that in turn cannot be understood without the motivation that drove it, which was a profound anxiety and distress over where humans ultimately stood in the order of things, and especially the temporal order of things.
If, in pre-modernity, time was governed by stable cycles and repetition (of monarchic succession, of seasonal change, of flooding rivers), modernity changed the shape of time from a circle to an arrow - a past back there, a present now, a future, way out that way (the eschatological religions helped alot to bring this change about). The future no longer guaranteed by the cycles to which it had always been tethered, it is humans who become responsible for time: it is only what they do that determines the success of failure of what happens next. And this is as liberatory and it is terrifying. So to your author's focus on progress, I would add and supplement Stanley Cavell's focus on existence itself becoming problematic:
"The modern [is] ... a moment in which history and its conventions can no longer be taken for granted; the time in which music and painting and poetry (like nations) have to define themselves against their pasts; the beginning of the moment in which each of the arts becomes its own subject, as if its immediate artistic task is to establish its own existence. The new difficulty which comes to light in the modernist situation is that of maintaining one’s belief in one’s own enterprise, for the past and the present become problematic together. The modernist difficulty... is the difficulty of making one’s present effort become a part of the present history of the enterprise to which one has committed one’s mind, such as it is". (Cavell, Must We Mean What We Say)
All this is to say that the flip-side of mastery is a deep worry about non-mastery, of being swallowed up by an inexorable march of forward-facing time that threatens at every point to render any achievement meaningless (lost to time). Consider some famous modernist figures: Kafka, Beckett, Joyce, Mondrian, Dickinson, Rimbaud - these are authors and artists whose works are filled with a kind of frazzled disorientation, and rather than reflect any triumphalism over the world, express a deep unease with it. So progress and mastery, yes. But also (and underlying the need for progress) - deep and yawning anxiety. Or to quote Shoshana Felman: "Modernity inheres in its own problematic status. The energy
that destabilizes it is the energy of a relentless, never-ending question" ("You Were Right To Leave, Arthur Rimbaud: Poetry and Modernity" - my favourite essay on this subject).