Side note: VMware ESX was a Linux based OS (yes, vmlinuz loaded vmware via kernel modules, not the other way around as VMware likes to tell people, you can see this if you watch ESX boot).
This is a persistent and incorrect story. The proprietary esx kernel takes over from the initial linux boot. The esx kernel schedules running VMs, not the linux kernel.
That may or may not be true, but it doesn't affect that the Linux kernel module interface is a really bad place to put your valuable, proprietary, until ESXi not-ported-elsewhere IP.
I did some development for that, it is based on Redhat.
I think their claim is that once the vmware modules load, they insert themselves under the Linux kernel (so Linux then acts like a dom0, similar to how Xen uses it). In that case, it would be in concept the same as one Linux kernel booting, and kexec'ing a second kernel.