The author says multiple times: "an acceleration of [X] km/s is required", maybe they meant to imply that the magnitude of the change of the velocity?

Accelerating at some rate km/ss for a period of s results in km/s. So the net result of "an acceleration" can be expressed as a velocity.

(what it comes down to is that "an" is an indefinite article and always modifies a noun and km/ss is described by the verb acceleration. Yay English.)

If i go from at rest (0m/s) to walking at 2m/s, I've completed an acceleration of 2m/s.

Delta-v is common in orbital mechanics, which is often referred as "an acceleration".