(Sorry for the long post, its my instructor background, and others may not know this. Generators are confusing)
What is required is a grounding electrode system, which can be a ground rod or rods, or perhaps the foundation the generator could qualify as a concrete encased electrode (no ground rods required for that system)
The rules are laid out in 250.30 and its section 4. This is longish section, if you are not familiar with it take some notes as you go.
Typically the connection to the grounding electrode system is made where the system bonding jumper is installed. Although this graphic shows a TS, it is a SDS due to the neutral being transferred, Also see 250.35(A) and this is IN #1 in 250.30
This is the SDS defintion