They could also just be spawning Windows VMs directly in AWS, no point doing nested virtualization for something like this. Pretty sure they have a service for doing exactly what you described. No need for a VPN, it can spawn your VM on the right network already (they call it VPC). They can even put real GPUs for AutoCAD and stuff on those things.
AWS does have plenty of VPN solutions for this, but likely not with the credentials you have because they’re usually very specific. And it’s probably intentional, if they wanted to give you VPN access they’d give you VPN access.