I can start my sump pump on a 1000W inverter and car battery, so I am
assuming I can start it from the 2000W generator, which has its own
inverter.

The reason I can see that they use two is that (apart from more power)
they get a parallel cable which has a large round generator cable
socket, which can be used to plug into the transfer switch. If I am
guessing right I can just build a regular cable with a 3-pin plug and
use that.