Intel P3 introduced SSE. The P4 SSE2.
Athlon XP doesn't support SSE2
It's easier to use CPU-Z than to try to remember.
Vmware since newer than Vmware 12.5.9 requires VT-X so it uses your host processor. Since all host processors that use VT-X currently support SSE2 then software requiring SS2 will work assuming no bugs with the software.
The same would apply to Vmware Fusion or Virtualbox.
If you want to test for SSE issues with software then best to use real hardware or pcem. This is helpful since compilers and libraries no longer test for lack of SSE,SSE2 and it can be difficult to track down why something isn't working.
As for the Roytam1 Pale Moon aka New Moon. Please don't call it Pale Moon. The Pale Moon devs haven acted very poorly on how they've hounded roytam1 for forking and supporting old operating systems. He's currently deciding on what the new name and branding will be.