Welcome to the Community - What you describe work - you can use LogMeIn to login directly into the XP machine and the workers access the old application - what ESXi sever cannot do is access the VMs from the server itself.
You could also VMware Workstation or VMware player and set up a similar conifugration - but you will need a machine that is running either WIndows or Linux as the host OS since these are hosted virtualization solutions
