Many would consider essential characteristics of what we commonly refer to as modern computers to include storage of programs in memory, digital rather than analog storage and computation, and general purpose computations (apart from finiteness limitations, any mathematically computable function can be computed on the machine). It thus stretches the definition to say that “in essence a computer is merely a special kind of Jacquard loom,” as Essinger claims.
Jacquard’s loom is a fascinating invention, and the use of punched cards to control it (even if only in fixed sequences, without conditional branches) was indeed a significant and important contribution to the history of computation. In addition to a detailed depiction of Jacquard’s life and work, the book covers Babbage and his computational engines, Hollerith and tabulating machines, the birth of IBM, and the development of the Harvard Mark I.
Those interested in the history of computation will find a readable exposition here, with some new information (especially from recently discovered correspondence between Ada Augusta and Charles Babbage) not found in some other treatments. However, the technical and scientific details could be stronger. Overall, I recommend the book.