First, there are many language who’s default integer type are not fixed bit width. For example Haskell and Python can represent arbitrarily large integers out of the box, limited only by available memory. Second, it is not too difficult to implement these “big integers” in any language. For example, I think java has something called a BigInteger class. Arguably if your “integer” type has fixed but width, it’s categorically not an integer. Third, two of the major underlying theoretical models of computation, Turing machines and Churche’s lambda calculus, allow arbitrary “memory” sizes and arbitrarily large integers. For example the universal Turing machine is imagined as operating over an infinitely long ticker tape. The objection you raise is a theoretical nonissue and I give the author some leeway to make this concept more accessible.