As of 2014, without performing unauthorized modifications to the Xbox 360 console, it is impossible to play a game intended for PC on an Xbox 360. This is largely due to Microsoft's desire to control what content is available to run on its system through its DRM policies.
Though the system architecture is very similar to that of a PC, Microsoft's policy on digital rights management exists to control what software may run on its console. This policy exists partly for quality assurance, in that any software released for the console can be expected to have achieved a certain level of performance, and to be compatible with the system. It also serves to give Microsoft partial control over the software published for its system. While the Xbox 360 may technically have the architecture to run many PC games, Microsoft's policy would never allow this to happen on an unmodified console.