1. U.S. Department of Energy, Federal Energy Management Program (FEMP). (2009). O&M Best Practices Guide for Standby Generators, Release 3.0, Chapter 2, Page 2.1.
The document states: "A standby generator set (genset) is the combination of an internal combustion engine and an electrical generator (alternator) that are coupled and mounted on a single frame." This directly supports the definition in the question.
2. Geng, H. (2014). Data Center Handbook. John Wiley & Sons, Inc. Chapter 10.3.1, "Standby Generators," Page 211.
This academic and professional handbook describes the system: "A standby generator system consists of a prime mover, an alternator, a cooling system, and a control system... The prime mover and alternator are coupled and mounted on a steel frame to form a generator set, or genset."
3. Iowa State University. (n.d.). Courseware for ABE 471/571: Electric Power and Electronics. Module: Standby Power. Section: "Components of a Standby System."
The course material explains: "The generator set, or 'genset', is the heart of the standby system. It consists of an engine mechanically coupled to an AC alternator, both of which are mounted on a common base."