Does IBM main frame 360 work similar to the new virtual desktops?

Kind of. Due to changes in the processor instruction set, later models of the IBM System/360 were able to utilize full virtualization, similar to what x86 processors with the Intel VT/AMD-V extension can utilize today. The System/360-67, the first model which could utilize virtualization, ran an operating system called CP/CMS, which was revolutionary at the time, since it divided each user session in such a way that an issue in one user session could not crash another user's session. Each user session ran on its own virtual machine with its own copy of the operating system, with all of these machines being controlled by a central control program. This hypervisor-virtual machine arrangement is extremely similar to how bare-metal virtualization products (VMWare's ESX Server, Citrix's Xen and derivative products) work today. In terms of architecture, no, x86 isn't similar at all to what IBM used back then -- which is why it took x86 over 30 years longer to develop the same technology.