DMCA exceptions can be argued for every 3 years, but they also must be resupported by the arguing/supporting party for approval for renewal every 3 years.
I see the exception you are referring to:
“Computer programs and video games distributed in formats that have become obsolete and that require the original media or hardware as a condition of access, when circumvention is accomplished for the purpose of preservation or archival reproduction of published digital works by a library or archive. A format shall be considered obsolete if the machine or system necessary to render perceptible a work stored in that format is no longer manufactured or is no longer reasonably available in the commercial marketplace.”
Notice that this exemption is only valid if the original Xbox game requires the original hardware. If the Xbox game in question is playable/supported on the Xbox 360, then it is still illegal to circumvent the copy protection on the disc.